bluuebunny/crossref_metadata_2025 huggingface dataset:
An attempt to understand the four color problem
Authors: Haken Wolfgang
Published: May 2007

Is the recently obtained, computer‐aided proof of the Four Color Theorem an isolated phenomenon or is its combinatorial complexity typical for a significantly large class of mathematical problems? While it is too early to give a definite answer to this question, an informal discussion is undertaken in this article.
Graph reconstruction—a survey
Authors: Bondy J. A. , Hemminger R. L.
Published: May 2007

The Reconstruction Conjecture asserts that every finite simple undirected graph on three or more vertices is determined, up to isomorphism, by its collection of vertex‐deleted subgraphs. This article reviews the progress made on the conjecture since it was first formulated in 1941 and discusses a number of related questions.
Every (p, p‐2) graph is contained in its complement
Authors: Burns David , Schuster Seymour
Published: May 2007

The following is proved: If G is graph of order p (≥2) and size p‐2, then there exists an isomorphic embedding of G into its complement.
The graph isomorphism disease
Authors: Read Ronald C. , Corneil Derek G.
Published: May 2007

The graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP‐completeness. No efficient (i.e., polynomial‐bound) algorithm for graph isomorphism is known, and it has been conjectured that no such algorithm can exist. Many papers on the subject have appeared, but progress has been slight; in fact, the intractable nature of the problem and the way that many graph theorists have been led to devote much time to it, recall those aspects of the four‐color conjecture which prompted Harary to rechristen it the “four‐color disease.” This paper surveys the present state of the art of isomorphism testing, discusses its relationship to NP‐completeness, and indicates some of the difficulties inherent in this particularly elusive and challenging problem. A comprehensive bibliography of papers relating to the graph isomorphism problem is given.
Line pseudodigraphs
Authors: Hemminger Robert L. , Klerlein Joseph B.
Published: May 2007

A new definition of the line digraph is given that reflects all types of arc adjacencies in the original digraph. The definition also allows for loops and multiple arcs, hence it is called the line pseudodigraph. A Whitney type theorem is then given; that is, the relationship between pseudodigraphs having the same line pseudodigraph is determined.
Hamiltonian cycles in cayley color graphs
Authors: Klerlein Joseph B.
Published: May 2007

A group Γ is said to possess a hamiltonian generating set if there exists a minimal generating set Δ for Γ such that the Cayley color graph DΔ(Γ) is hamiltonian. It is shown that every finite abelian group has a hamiltonian generating set. Certain classes of nonabelian groups are also investigated.
On stable crossing numbers
Authors: Kainen Paul C. , White Arthur T.
Published: May 2007

Results giving the exact crossing number of an infinite family of graphs on some surface are very scarce. In this paper we show the following: for G = Qn × K4.4, cry(G)‐m(G) = 4m, for 0 ⩽ = m ⩽ 2n. A generalization is obtained, for certain repeated cartesian products of bipartite graphs. Nonorientable analogs are also developed.
An upper bound on the size of a largest clique in a graph
Authors: Geoffroy Dennis P. , Sumner David P.
Published: May 2007

A graph is point determining if distinct vertices have distinct neighborhoods. The nucleus of a point‐determining graph is the set GO of all vertices, v, such that G–v is point determining. In this paper we show that the size, ω(G), of a maximum clique in G satisfies ω(G) ⩽ 2|π (G)O|, where π(G) (the point determinant of G) is obtained from G by identifying vertices which have the same neighborhood.
A note on graphs spanned by Eulerian graphs
Authors: Pulleyblank W. R.
Published: May 2007

We show that the problem raised by Boesch, Suffel, and Tindell of determining whether or not a graph is spanned by an Eulerian subgraph is NP‐complete. We also note that there does exist a good algorithm for determining if a graph is spanned by a subgraph having positive even degree at every node.
Every connected, locally connected nontrivial graph with no induced claw is hamiltonian
Authors: Oberly David J. , Sumner David P.
Published: May 2007

A graph is locally connected if every neighborthood induces a connected subgraph. We show here that every connected, locally connected graph on p ≥ 3 vertices and having no induced K1,3 is Hamiltonian. Several sufficient conditions for a line graph to be Hamiltonian are obtained as corollaries.
A class of upper‐embeddable graphs
Authors: Jaeger F. , Payan C. , Xuong N. H.
Published: May 2007

In this paper, we prove the following result: Every graph obtained by connecting (with any number of edges) two vertex‐disjoint upper‐embeddable graphs graphs with even Betti number is upper‐embeddable.
Separation of graphs into three components by the removal of edges
Authors: Goldsmith Donald L. , Manvel Bennet , Faber Vance
Published: May 2007

Several ways to separate a connected graph into three components by the removal of edges are discussed. Graphical parameters that count the number of edges removed are introduced and the relations between these parameters are given.
A characterization of ptolemaic graphs
Authors: Howorka Edward
Published: May 2007

A connected graph G is ptolemaic provided that for each four vertices Ui, 1 ≤ i ≤ 4, of G, the six distances dii = dG (Ui, Ui), i ≠ j satisfy the inequality d12d34 ≤ d13d24 + d14d23 (shown by Ptolemy to hold in Euclidean spaces). Ptolemaic graphs were first investigated by Chartrand and Kay, who showed that weakly geodetic ptolemaic graphs are precisely Husimi trees (in particular, trees are ptolemaic). in the present paper several characterizations of ptolemaic graphs are given. It is shown, for example, that a connected graph G is ptolemaic if and only iffor each nondisjoint cliques P, Q of G, their intersection is a cutset of G which separates P‐Q and Q‐P. An operation is exhibited which generates all finite ptolemaic graphs from complete graphs.
Maximal non‐ hamilton‐laceable graphs
Authors: Simmons Gustavus J.
Published: May 2007

For bipartite graphs the property of being Hamilton laceable is analogous to the property of being Hamilton connected for simple graphs. in this paper it is proven that all of the graphs obtained by deleting fewer than m − 1 edges from either of the complete bipartite graphs Km, m or Km, m+1 are Hamilton laceable. It is also proven that the deletion of m − 1 edges results in a non‐Hamiltonlaceable graph if and only if the graph is either the complement of the star K1,m−1 in Km, m or Km, m+1 or else the complement in K3,3 of a pair of nonadjacent edges.
Generating all 4‐regular planar graphs from the graph of the octahedron
Authors: Lehel Jenö
Published: May 2007

It has been communicated by P. Manca in this journal that all 4‐regular connected planar graphs can be generated from the graph of the octahedron using simple planar graph operations. We point out an error in the generating procedure and correct it by including an additional operation.
A remark on the factor theorems of lovász and tutte
Authors: Thomassen Carsten
Published: May 2007

We present a short proof of factor theorems of Lovász and Tutte.
Harmonious labelings of windmill graphs and related graphs
Authors: Hsu D. Frank
Published: May 2007

A strongly harmonious labeling is the nonmodular version of a harmonious labeling. The windmill graph K(t)n is the graph consisting of t copies of the complete graph Kn with a vertex in common. It is shown that, for t ≥ 1, K(t)n is strongly harmonious and so harmonious by drawing on partitions already available from the construction of cyclic neofields. Other irregular windmill graphs can be shown to be strongly harmonious in a similar way.
Counterexamples to randić's conjecture on distance degree sequences for trees
Authors: Slater Peter J.
Published: May 2007

As counterexamples to a conjecture of Randić, pairs of nonisomorphic trees with the same collections of distance degree sequences are presented.
On maximum bipartite subgraphs
Authors: Malle Günther
Published: May 2007

In this paper are investigated maximum bipartite subgraphs of graphs, i.e., bipartite subgraphs with a maximum number of edges. Such subgraphs are characterized and a criterion is given for a subgraph to be a unique maximum bipartite subgraph of a given graph. In particular maximum bipartite subgraphs of cubic graphs are investigated. It is shown that cubic graphs can be built up from five building stones (called elementary paths). Finally the investigation of a special class of cubic graphs yields a theorem which characterizes the Petersen graph and the dodecahedron graph by means of their maximum bipartite subgraphs.
Extremal bipartite subgraphs of cubic triangle‐free graphs
Authors: Hopkins Glenn , Staton William
Published: May 2007

A cubic triangle‐free graph has a bipartite subgraph with at least 4/5 of the original edges. Examples show that this is a best possible result.
Maximum k‐colorable subgraphs
Authors: Locke S. C.
Published: May 2007

A lower bound is established on the number of edges in a maximum k‐colorable subgraph of a loopless graph G. For the special case of 3‐regular graphs, lower bounds are also determined on the maximum number of edges in a bipartite subgraph whose color classes are of equal size.
Vertices of given degree in a random graph
Authors: Bollobás Béla
Published: May 2007

This paper concerns the degree sequence d1 ≥ d2 ≥ … ≥ dn of a randomly labeled graph of order n in which the probability of an edge is p(n) ≦ 1/2. Among other results the following questions are answered. What are the values of p(n) for which d1, the maximum degree, is the same for almost every graph? For what values of p(n) is it true that d2 > d2 for almost every graph, that is, there is a unique vertex of maximum degree? The answers are (essentially) p(n) = o(logn/n/n) and p(n)n/logn → ∞. Also included is a detailed study of the distribution of degrees when 0 < lim n p(n)/log n ≦ lim n p(n)/log n < ∞.
A shortness exponent for r‐regular r‐connected graphs
Authors: Jackson Brad , Parsons T. D.
Published: May 2007

Let r≧ 3 be an integer. It is shown that there exists ε= ε(r), 0 < ε < 1, and an integer N = N(r) > 0 such that for all n ≧ N (if r is even) or for all even n ≧ N(if r is odd), there is an r‐connected regular graph of valency r on exactly n vertices whose longest cycles have fewer than nε vertices.
Every simple 3‐polytope of order 32 or less is Hamiltonian
Authors: Okamura Haruko
Published: May 2007

Using theorems of Butler, Goodey, and Okamura we show that every simple 3‐polytope of order 32 or less is Hamiltonian.
Graphs with nilpotent adjacency matrices
Authors: Liebeck Martin W.
Published: May 2007

Given any integer t ≥ 2 and any prime number p, a graph Γp,t is constructed whose adjacency matrix is nilpotent of index t over Zp' the field of p elements.
The number of tournaments with a unique spanning cycle
Authors: Moon J. W.
Published: May 2007

The number of tournaments Tn on n nodes with a unique spanning cycle is the (2n‐6)th Fibonacci number when n ≥ 4. Another proof of this result is given based on a recursive construction of these tournaments.
Atoll decompositions of graphs
Authors: Buckley Fred
Published: May 2007

An island decomposition of a graph G consists of a set of vertex‐disjoint paths which cover the vertex set of G. If the endpoints of the paths are mutually nonadjacent, then we have an atoll decomposition. We characterize graphs requiring two paths in an island decomposition yet having no atoll decomposition. Results are given relating atoll decompositions to cutpoints and Hamiltonian blocks.
Bounds for the ramsey number of a disconnected graph versus any graph
Authors: Gould Ronald J. , Jacobson Michael S.
Published: May 2007

Bounds are determined for the Ramsey number of the union of graphs versus a fixed graph H, based on the Ramsey number of the components versus H. For certain unions of graphs, the exact Ramsey number is determined. From these formulas, some new Ramsey numbers are indicated. In particular, ifmagnified image.

Where ki is the number of components of order i and t1 (H) is the minimum order of a color class over all critical colorings of the vertices of H, thenmagnified image.
A new 5‐arc‐transitive cubic graph
Authors: Biggs N. L.
Published: May 2007

A connected cubic graph with 2352 vertices is constructed and is shown to have a group of automorphisms which acts transitively on the 5‐arcs. The construction requires only elementary properties of the Fano plane.
A cubic 3‐connected graph having no cycle through given 10 vertices has the “Petersen form”
Authors: Kelmans A. K. , Lomonosov M. V.
Published: May 2007

It has been proved [1,2] that in a cubic 3‐connected graph any 9 vertices lie on a common cycle.
Geodesic subgraphs
Authors: Batten Lynn Margaret
Published: May 2007

Define a geodesic subgraph of a graph to be a subgraph H with the property that any geodesic of two points of H is in H. The trivial geodesic subgraphs are the complete graphs Kn' n ≧ 0, and G itself. We characterize all (finite, simple, connected) graphs with only the trivial geodesic subgraphs, and give an algorithm for their construction. We do this also for triangle‐free graphs.
Interpolation theorem for the number of end‐vertices of spanning trees
Authors: Schuster Seymour
Published: May 2007

The following interpolation theorem is proved: If a graph G contains spanning trees having exactly m and n end‐vertices, with m < n, then for every integer k, m < k < n, G contains a spanning tree having exactly k end‐vertices. This settles a problem posed by Chartrand at the Fourth International Conference on Graph Theory and Applications held in Kalamazoo, 1980.
Regular graphs with given girth pair
Authors: Harary Frank , Kovács Peter
Published: May 2007

The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair is proved and simple bounds for their smallest order are developed. Several infinite classes of such graphs are constructed and it is proved that two of these families consist of smallest graphs.
On the average shape of simply generated families of trees
Authors: Kirschenhofer Peter
Published: May 2007

This paper deals with the limiting distribution of the level number of the jth leaf of a planted plane tree (where leaves are enumerated from left to right) for the so‐called “simply generated families” introduced by Meir and Moon. The mathematical apparatus is determined by the idea of an asymptotic analysis of a given sequence of numbers by studying the location and nature of the singularities of appropriate generating functions.
Embeddings of bipartite graphs
Authors: Abu‐Sbeih Mohammed , Parsons T. D.
Published: May 2007

If G is a bipartite graph with bipartition A, B then let Gm,n(A, B) be obtained from G by replacing each vertex a of A by an independent set a1, …, am, each vertex b of B by an independent set b1,…, bn, and each edge ab of G by the complete bipartite graph with edges aibj (1 ≤ i ≤ m and 1 ≤ j ≤ n). Whenever G has certain types of spanning forests, then cellular embeddings of G in surfaces S may be lifted to embeddings of Gm,n(A, B) having faces of the same sizes as those of G in S. These results are proved by the technique of “excess‐current graphs.” They include new genus embeddings for a large class of bipartite graphs.
Partitioning oriented 2‐paths
Authors: Heinrich Katherine
Published: May 2007

There are three types of oriented 2‐paths. Necessary and sufficient conditions are given under which all oriented 2‐paths of the same type and with vertices labeled 1, 2,…., n can be partitioned into copies of the complete symmetric directed graph with n vertices.
On Ramsey numbers involving starlike multipartite graphs
Authors: Burr S. A. , Faudree R. J. , Rousseau C. C. , Schelp R. H.
Published: May 2007

The Ramsey number r(G, H) is evaluated exactly in certain cases in which both G and H are complete multipartite graphs K(n,1, n2, …. nk). Specifically, each of the following cases is handled whenever n is sufficiently large: r(K(1, m1, …. mk), K(1, n)), r(K(1, m), K(n1, …. nk, n)), provided m ≧ 4, and r(K(1, 1, m), K(nk, …, nk, n)).
On the notion of infinite Hamiltonian graph
Authors: Halin R.
Published: May 2007

Based on the terms “end” and “cofinal spanning subtree” a general notion of Hamiltonicity of infinite graphs is developed. It is shown that the cube of every connected locally finite graph is Hamiltonian in this generalized sense.
Knots and links in spatial graphs
Authors: Conway J. H. , McA. Gordon C.
Published: May 2007

The main purpose of this paper is to show that any embedding of K7 in three‐dimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of K6 contains a pair of disjoint cycles which are homologically linked.
Numbers of cubic graphs
Authors: Robinson R. W. , Wormald N. C.
Published: May 2007

The numbers of unlabeled cubic graphs on p = 2n points have been found by two different counting methods, the best of which has given values for p ≦ 40.
A generalization of chordal graphs
Authors: Seymour P. D. , Weaver R. W.
Published: May 2007

In a 3‐connected planar triangulation, every circuit of length ≥ 4 divides the rest of the edges into two nontrivial parts (inside and outside) which are “separated” by the circuit. Neil Robertson asked to what extent triangulations are characterized by this property, and conjectured an answer. In this paper we prove his conjecture, that if G is simple and 3‐connected and every circuit of length ≥ 4 has at least two “bridges,” then G may be built up by “clique‐sums” starting from complete graphs and planar triangulations. This is a generalization of Dirac's theorem about chordal graphs.
On smallest regular graphs with a given isopart
Authors: Fink John Frederick
Published: May 2007

For a nonempty graph, G, we define p(G) and r(G) to be respectively the minimum order and minimum degree of regularity among all connected regular graphs H having a nontrivial decomposition into subgraphs isomorphic to G. By f(G), we denote the least integer t for which there is a connected regular graph H having a decomposition into t subgraphs isomorphic to G. In this article, the values of these parameters are determined for complete graphs, cycles, and stars. Furthermore, we show that Δ(T) ⩽ r(T) ⩽ δ (T) + 1 for every tree T. and r(T) Δ(T) if the maximum degree Δ(T) is even.
Rao's conjecture on self‐complementary graphs with K‐factors
Authors: Ando Kiyoshi
Published: May 2007

Rao posed the following conjecture, “Let G be a self‐complementary graph of order p, π = (d1 … dp) be its degree sequence. Then G has a k‐factor if and only if π − k, = (d1 − k, … dP − k) is graphical.” We construct a family of counterexamples for this conjecture for every k ⩾ 3.
[a,b]‐factorization of a graph
Authors: Kano Mikio
Published: May 2007

Let a and b be integers such that 0 ⩽ a ⩽ b. Then a graph G is called an [a, b]‐graph if a ⩽ dG(x) ϵ b for every x ϵ V(G), and an [a, b]‐factor of a graph is defined to be its spanning subgraph F such that a ⩽ dF(x) ⩽ b for every vertex x, where dG(x) and dF(x) denote the degrees of x in G and F, respectively. If the edges of a graph can be decomposed into [a.b]‐factors then we say that the graph is [2a, 2a]‐factorable. We prove the following two theorems: (i) a graph G is [2a, 2b)‐factorable if and only if G is a [2am,2bm]‐graph for some integer m, and (ii) every [8m + 2k, 10m + 2k]‐graph is [1,2]‐factorable.
Packing a tree with a graph of the same size
Authors: Slater P. J. , Teo S. K. , Yap H. P.
Published: May 2007

We prove that if T is a tree of order p ⩾ 5 and G is a graph of order p and size p ‐ 1 such that neither T nor G is a star, then T can be embedded in G, the complement of G.
Threshold characterization of graphs with dilworth number two
Authors: Benzaken C. , Hammer P. L. , de Werra D.
Published: May 2007

A graph with nodes 1, …, n is a threshold signed graph if one can find two positive real numbers S, T and real numbers a1, …, an associated with the vertices in such a way that i, j are linked iff either |ai + aj| ≥ S or |ai ‐ aj| ≥ T. Such graphs generalize threshold graphs. It is shown that these graphs are precisely the graphs with Dilworth number at most two (the Dilworth number is the maximum number of pairwise incomparable vertices in the vicinal preorder). Some other properties of this subclass of perfect graphs are also presented. The graphs considered in this paper are finite simple graphs G = (V, E), where V is the vertex set of G and E a subset of pairs of G. For x V, N(x) denotes the neighbor set of x: N(x) = {y | {x, y} E}.
Longest paths and cycles in K1,3‐free graphs
Authors: Matthews Manton M. , Sumner David P.
Published: May 2007

In this article we show that the standard results concerning longest paths and cycles in graphs can be improved for K1,3‐free graphs. We obtain as a consequence of these results conditions for the existence of a hamiltonian path and cycle in K1,3‐free graphs.
The frame dimension and the complete overlap dimension of a graph
Authors: Steif Jeffrey E.
Published: May 2007

Roberts (F. S. Roberts, On the boxicity and cubicity of a graph. In Recent Progress in Combinatorics, W. T. Tutte, ed. Academic, New York (1969)), studied the intersection graphs of closed boxes (products of closed intervals) in Euclidean n‐space, and introduced the concept of the boxicity of a graph G, the smallest n such that G is the intersection graph of boxes in n‐space. In this paper, we study the intersection graphs of the frames or boundaries of such boxes. We study the frame dimension of a graph G—the smallest n such that G is the intersection graph of frames in n‐space. We also study the complete overlap dimension of a graph, a notion that is almost equivalent. The complete overlap dimension of a graph G is the smallest dimension in which G can be represented by boxes that intersect but are not completely contained in one another. We will prove that these dimensions are in almost all cases the same and that they both can become arbitrarily large. We shall also obtain a bound for these dimensions in terms of boxicity.
A note on the matching numbers of triangle‐free graphs
Authors: Frucht Roberto W. , Giudici Reinaldo E.
Published: May 2007

For the sake of brevity the absolute values of the coefficients of the matching polynomial of a graph are called matching numbers in this note. It is shown that for a triangle‐free graph these numbers coincide with the coefficients of the chromatic polynomial of its complement when this polynomial is written in factorial form.

As an application it is mentioned that the coefficients of every rook polynomial are at the same time coefficients of some chromatic polynomial.
Families of graphs complete for the strong perfect graph Conjecture
Authors: Corneil D. G.
Published: May 2007

The Strong Perfect Graph Conjecture states that a graph is perfect iff neither it nor its complement contains an odd chordless cycle of size greater than or equal to 5. In this article it is shown that many families of graphs are complete for this conjecture in the sense that the conjecture is true iff it is true on these restricted families. These appear to be the first results of this type.
Asymptotic enumeration of labeled multigraphs by vertices, edges, and degree parities
Authors: Bender Edward A. , Bruce Richmond L.
Published: May 2007

We show that the number of labeled (n, q)‐multigraphs with some specified p vertices of odd degree is asymptotically independent of p and is in fact asymptotically 21−n times the number of (n, q)‐multigraphs. We determine the asymptotic number of (n, q)‐multigraphs.
Convex labelings of trees
Authors: Dow Stephen J. , Rall Douglas F. , Slater Peter J.
Published: May 2007

A convex labeling of a tree T of order n is a one‐to‐one function f from the vertex set of T into the nonnegative integers, so that f(y) ⩽ (f(x) + f(z))/2 for every path x, y, z of length 2 in T. If, in addition, f(v) ⩽ n − 1 for every vertex v of T, then f is a perfect convex labeling and T is called a perfectly convex tree. Jamison introduced this concept and conjectured that every tree is perfectly convex. We show that there exists an infinite class of trees, none of which is perfectly convex, and in fact prove that for every n there exists a tree of order n which requires a convex labeling with maximum value at least 6n/5 – 22. We also prove that every tree of order n admits a convex labeling with maximum label no more than n2/8 + 2. In addition, we present some constructive methods for obtaining perfect convex labelings of large classes of trees.
A sufficient condition for a digraph to be kernel‐perfect
Authors: Duchet P.
Published: May 2007

Galeana‐Sanchez and Neumann‐Lara proved that a sufficient condition for a digraph to have a kernel (i.e., an absorbent independent set) is the following: (P) every odd directed cycle possesses at least two directed chords whose terminal endpoints are consecutive on the cycle. Here it is proved that (P) is satisfied by those digraphs having these two properties: (i) the reversal of every 3‐circuit is present, and (ii) every odd directed cycle v1… v2n+1 V1 has two chords of the form (vi, vi+2). This is stronger than a result of Galeana‐Sanchez.
Panel studies in developing countries: case analysis of sample attrition over the past 16 years within the birth to twenty cohort in Johannesburg, South Africa
Authors: Norris Shane A. , Richter Linda M. , Fleetwood Stella A.
Published: May 2007

The implementation of panel studies in developing countries can prove valuable in driving evidenced‐based policies. Case analysis from panel studies in developing countries are therefore useful in offering guidance and insight to deal with the immense challenges of implementing and following‐up a panel study in a developing country. The aim of this paper is to describe the follow‐up process within Birth to Twenty (Bt20), a birth cohort study in Johannesburg, South Africa, over the past 16 years; and to outline retention strategies and insight within the context of an urban, developing country setting. The main issues considered are: attrition (periodic and absolute), movement of individuals, name changes, cohort management and lessons learned. Copyright © 2007 John Wiley & Sons, Ltd.
From marine ecology to crime analysis: Improving the detection of serial sexual offences using a taxonomic similarity measure
Authors: Woodhams Jessica , Grant Tim D. , Price Andrew R. G.
Published: June 2007

Jaccard has been the choice similarity metric in ecology and forensic psychology for comparison of sites or offences, by species or behaviour. This paper applies a more powerful hierarchical measure—taxonomic similarity (Δs), recently developed in marine ecology—to the task of behaviourally linking serial crime. Forensic case linkage attempts to identify behaviourally similar offences committed by the same unknown perpetrator (called linked offences). Δs considers progressively higher‐level taxa, such that two sites show some similarity even without shared species. We apply this index by analysing 55 specific offence behaviours classified hierarchically. The behaviours are taken from 16 sexual offences by seven juveniles where each offender committed two or more offences. We demonstrate that both Jaccard and Δs show linked offences to be significantly more similar than unlinked offences. With up to 20% of the specific behaviours removed in simulations, Δs is equally or more effective at distinguishing linked offences than where Jaccard uses a full data set. Moreover, Δs retains significant difference between linked and unlinked pairs, with up to 50% of the specific behaviours removed. As police decision‐making often depends upon incomplete data, Δs has clear advantages and its application may extend to other crime types. Copyright © 2007 John Wiley & Sons, Ltd.
Statistical downscaling of precipitation for a selection of sites in Ireland employing a generalised linear modelling approach
Authors: Fealy Rowan , Sweeney John
Published: May 2007

Producing plausible outputs from statistically downscaled models of daily precipitation remains a significant challenge when producing climate scenarios for impact assessments. This challenge arises primarily as a consequence of a number of difficulties encountered when working with higher resolution daily precipitation data. Precipitation receipts at a site tend to be largely heterogeneous over space and time as local factors, such as relief, play an important role in determining whether it rains or not. More crucially from the point of view of statistical analysis, daily precipitation data is rarely, if ever, normally distributed, resulting from a high frequency occurrence of low‐fall events and a low frequency of high‐fall events. Additionally, modelling precipitation requires a two‐step procedure. First, precipitation occurrence must be modelled: then a model is fitted to precipitation quantities which describes the rainfall distribution for days on which precipitation occurs. This paper presents a technique that overcomes some of the difficulties encountered and produces plausible precipitation amounts for a selection of 14 sites in Ireland. Difficulties still exist with predicting extreme precipitation events, which tend to be underestimated by the methodology employed. Copyright © 2007 Royal Meteorological Society
Wheat response to N2 fixed by faba bean (Vicia faba L.) as affected by sulfur fertilization and rhizobial inoculation in semi‐arid Northern Ethiopia
Authors: Habtegebrial Habtemichial Kiros , Ram Singh Bal , Aune Jens Bernt
Published: May 2007

Nitrogen fixation in faba bean (Vicia faba cv. Mesay) as affected by sulfur (S) fertilization (30 kg S ha–1) and inoculation under the semi‐arid conditions of Ethiopia was studied using the 15N‐isotope dilution method. The effect of faba bean–fixed nitrogen (N) on yield of the subsequent wheat crop (Triticum aestivum L.) was also assessed. Sulfur fertilization and inoculation significantly (p < 0.05) affected nodulation at late flowering stage for both 2004 and 2005 cropping seasons. The nodule number and nodule fresh weighs were increased by 53% and 95%, relative to the control. Similarly, both treatments (S fertilization and inoculants) significantly improved biomass and grain yield of faba bean on average by 2.2 and 1.2 Mg ha–1. This corresponds to 37% and 50% increases, respectively, relative to the control. Total N and S uptake of grains was significantly higher by 59.6 and 3.3 kg ha–1, which are 76% and 66% increases, respectively. Sulfur and inoculation enhanced the percentage of N derived from the atmosphere in the whole plant of faba bean from 51% to 73%. This corresponds to N2 fixation varying from 49 to 147 kg N ha–1. The percentage of N derived from fertilizer (%Ndff) and soil (%Ndfs) of faba bean varied from 4.3% to 2.8 %, and from 45.1% to 24.0%, corresponding to the average values of 5.1 and 47.9 kg N ha–1. Similarly, the %Ndff and %Ndfs of the reference crop, barley, varied from 8.5 % to 10.8% and from 91.5% to 89.2%, with average N yields of 9.2 and 84.3 kg N ha–1. Soil N balance after faba bean ranged from 13 to 52 kg N ha–1. Beneficial effects of faba bean on yield of a wheat crop grown after faba bean were highly significant, increasing the average grain and N yields of this crop by 1.11 Mg ha–1 and 30 kg ha–1, relative to the yield of wheat grown after the reference crop, barley. Thus, it can be concluded that faba bean can be grown as an alternative crop to fallow, benefiting farmers economically and increasing the soil fertility.
Differential accumulation patterns of phosphorus and potassium by canola cultivars compared to wheat
Authors: Rose Terry J. , Rengel Zed , Ma Qifu , Bowden John W.
Published: May 2007

The phosphorus (P) and potassium (K) accumulation patterns of canola (Brassica napus L.) are poorly understood, although such information is essential for determining optimal P‐ and K‐fertilizer strategies. This study investigated the patterns of P and K uptake and distribution among plant organs of three early or midmaturing canola cultivars (Tribune, Trigold, and Boomer) differing in K efficiency compared to wheat (Triticum aestivum L. cv. Nyabing). Plants were grown in a glasshouse with nonlimiting P and K supply and harvested at eight growth stages until maturity. Maximum P accumulation by all canola cultivars occurred during late flowering (GS 5,5; 84 d after sowing), whereas P accumulation in wheat plants peaked just prior to anthesis (Z59; 73 d after sowing). Maximum accumulation of K in canola cultivars Tribune and Trigold occurred 73 d after sowing (GS 4,8), but peaked earlier (61 d after sowing) in Boomer canola (GS 4,2) and Nyabing wheat (Z55). The results highlight the importance of early P and K supply to both species; however, the extended uptake of P and K by the canola cultivars Trigold and Tribune compared to wheat suggests that availability of soil P or K postflowering may be of more importance to canola than to wheat.
Relationships between desert dunes during the late Quaternary in the Lake Frome region, Strzelecki Desert, Australia
Authors: Fitzsimmons Kathryn E. , Bowler James M. , Rhodes Edward J. , Magee John M.
Published: June 2007

Transverse and linear dunes near the ephemeral Lake Frome in the Strzelecki Desert of Australia provide evidence for a genetic geomorphic relationship between desert dune types. Transverse dunes, overlying palaeoshorelines, lie upwind from linear dunes. The sedimentology of both dune types is similar, suggesting reworking or downwind transport of the same source material over time. Clay pellets from several horizons within the linear and transverse dunes provide evidence for fluctuating water tables and high evaporation rates during those periods of aeolian activity, along with salt influx associated with the deflation of Lake Frome. We conclude that the nature and initiation of dune activity is controlled not only by aridity, but by local hydrology. OSL ages from both transverse and linear dunes indicate aeolian activity at 66–57 ka and 22–11 ka. Transverse dune building took place around 106–111 ka. Linear dune activity initiated at least 66 ka ago, with reactivation around 43–28 ka, followed by pedogenesis in response to humid conditions. Widespread dune reactivation from around 22 ka correlates broadly with the Last Glacial Maximum and late glacial period, consistent with evidence of cold, arid conditions and dune activity in Australia. Copyright © 2007 John Wiley & Sons, Ltd.
Pre‐Quaternary landscape inheritance in Australia
Authors: Pillans Brad
Published: June 2007

Palaeogeographic reconstructions indicate that parts of the Australian continent have been subaerially exposed for hundreds of millions of years. Some landforms and regolith are demonstrated to be at least 300 million years old, but their persistence at or near the surface is inconsistent with long‐term denudation rate estimates based on cosmogenic nuclides and apatite fission track thermochronology. Burial and exhumation are suggested as significant preservation factors, in conjunction with prolonged tectonic stability and a shift to more arid climatic regimes in the Cenozoic. Copyright © 2007 John Wiley & Sons, Ltd.
On‐chip connector valve for immunoaffinity chromatography in a microfluidic chip
Authors: Shimura Kiyohito , Koyama Yutaka , Sato Kae , Kitamori Takehiko
Published: May 2007

A miniature valve that operates between a chip port and a tube fitting was developed. The valve functions by means of a rotor, 3 mm in diameter and 1.5 mm in height, made of Teflon, with a 0.2‐mm diameter hole at its center that is co‐axial with the tube fitting. It also has a radial groove, 0.85 mm long, 0.2 mm wide, and 0.2 mm deep, at the bottom surface, starting at its center. The chip port and the tube fitting have an offset of 0.75 mm, and, thus, the rotation of the rotor can make an on and off connection between the chip port and the groove, which is connected to the tubing. The valve had a pressure resistance of at least 1.0 MPa. The on‐chip valve can be placed in position by adding only a single part, a valve rotor, and no changes in the fabrication of the glass microchip are required. Since the valve functions as a part of a connector, we refer to it as an on‐chip connector valve. Immunoaffinity chromatography of a fluorescence‐labeled recombinant antibody fragment was carried out in a glass microchip using the valves.
Strong Market Growth in 2006 – World Market for Laser Systems Reaches New Record High
Authors: Mayer Arnold
Published: June 2007

In 2006, the world market volume of laser machining systems reached a new record high. After the record high in 2000 the market saw decreasing numbers first and recovered then in 2004 and 2005 to a level of 4.8 billion euro. In 2006 the market saw a remarkable 27 percent increase to 6.1 billion euro (Fig. 1).
In situ studies of the corrosion during drying of confined zinc surfaces
Authors: Persson D. , Mikhailov A. , Thierry D.
Published: June 2007

The corrosion process during the drying out of zinc surfaces confined in crevices was studied using real time photograpy and in situ FTIR microspectroscopy. A pH‐indicator was used to visualise differences in the pH during the drying process. The distribution and the composition of the corrosion products after several wetting and drying cycles were studied with FTIR microspectroscopy and SEM‐EDS. An area with high pH formed during the drying process at the border of the electrolyte, with a zone of white corrosion products that contained zinc hydroxycarbonate in the electrolyte inside this area. A differential aeration cell is present at the border of the electrolyte, and the cathodic oxygen reduction reaction takes place close to the border of the electrolyte during the drying process. The corrosion attack and the distribution and composition of the corrosion products on the surface depend strongly on the drying process of the surface. The corrosion attack of confined surfaces was localised, with a significantly higher corrosion attack in some areas. Outside the drying front a thin layer of electrolyte formed as a result of surface tension driven flow of electrolyte from the electrolyte border. This effect was attributed to the alkaline pH of the electrolyte due to the oxygen reduction reaction at the border. A galvanic element was formed between the local cathodes in the area outside the drying front and the anode in the area with bulk electrolyte. The main corrosion products detected after several wet dry cycles were ZnO, Zn5(OH)6(CO3)2 and Zn5(OH)8Cl2 · H2O, but Na2CO3 · 10H2O was also detected. The corrosion products were non‐homogeneously distributed on the surface and the distribution was related to the anodic and cathodic processes that took place in different regions on the surface during the corrosion process.
Selected Polymers that Contain Aromatic Ester Units: Synthesis, Photoreactions, and Refractive Index Modulation
Authors: Daschiel Ute , Höfler Thomas , Jakopic Georg , Schmidt Volker , Kern Wolfgang
Published: May 2007

Photoreactive polymers bearing aliphatic and aromatic esters of 4‐(N,N‐diphenylamino)phenol in the side chain, poly[4‐(N,N‐diphenylamino)phenyl acrylate] (P1) and poly[4‐(N,N‐diphenylamino)phenyl 4‐vinylbenzoate] (P2), are prepared from their monomers by free radical polymerization. In addition, poly[naphthalene‐1‐yl 4‐vinylbenzoate] is synthesized (P3). These materials absorb UV light up to λ = 350 nm. The polymers P1–P3 as well as low‐molecular‐weight model compounds are investigated with respect to their photoreactions under UV illumination. It is found that decarboxylation is the dominant reaction and that the photo‐Fries rearrangement occurs as a minor reaction. The fully aromatic ester units in P2 are more reactive than the ester units in P1. In the polymers, decarboxylation proceeds more efficiently than in the low‐molecular‐weight model compounds. Upon UV illumination of the polymers, large increases of the refractive index are observed (Δn450 up to +0.07). This is in agreement with the structural changes in the polymers after irradiation as calculated from group contributions to molar refraction. A preliminary investigation under 610 nm fs laser irradiation indicates that refractive index patterns can be produced by two‐photon effects (TPA). The polymers are of potential interest for applications in the field of optical waveguides.

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One‐Pot Synthesis of pH‐Responsive PEGylated Nanogels Containing Gold Nanoparticles by Autoreduction of Chloroaurate Ions within Nanoreactors
Authors: Oishi Motoi , Hayashi Hisato , Uno Teppei , Ishii Takehiko , Iijima Michihiro , Nagasaki Yukio
Published: May 2007

One‐pot synthesis of pH‐responsive PEGylated nanogels (diameter <100 nm) containing gold nanoparticles (AuNPs) was successfully carried out through the autoreduction of HAuCl4 with PEGylated nanogels constructed from cross‐linked poly[2‐(N,N‐diethylamino)ethyl methacrylate] (PDEAMA) core and tethered PEG chains. Transmission electron microscopy image of the nanogel containing AuNPs prepared at N/Au ratio = 8 revealed that the average number of AuNPs in a single nanogel and average diameter of the AuNPs were about 10 particles/nanogel and 6 nm, respectively. The surface plasmon band of the PEGylated nanogel containing AuNPs was shifted in response to pH, indicating that the cross‐linked PDEAMA core of the nanogels acts as not only nanoreactor but also pH‐sensitive matrix.

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AN INTERPRETATION OF MARTIN‐LÖF'S CONSTRUCTIVE THEORY OF TYPES IN ELEMENTARY TOPOS THEORY
Authors: Preller Anne
Published: May 2007

We give a formal interpretation of Martin‐Löf's Constructive Theory of Types in Elementary Topos Theory which is presented as a formalised theory with intensional equality of objects. Types are interpreted as arrows and variables as sections of their types. This is necessary to model correctly the working of the assumption x ∈ A. Then intensional equality interprets equality of types. The normal form theorem which asserts that the interpretation of a type is intensional equal to the pullback of its “alignment” along some “base” arrow relates this interpretation to categorical semantic of types.
AN ELEMENTARY SYSTEM AS AND ITS SEMI‐COMPLETENESS AND DECIDABILITY
Authors: Jun Qin
Published: May 2007

The author establishes an elementary system AS which contains functions +, ≐ and a constant 0 and then proves the semi‐completeness and the decidability of AS, using the theory of systems of inequalities.
A DIRECT PROOF OF A RESULT OF SHELAH
Authors: Weese Martin
Published: May 2007

Shelah has shown (see [1]) that the number d, the smallest cardinality of a dominating family, is less than or equal to the number i, the smallest cardinality of a maximal independent family on ω. This was done using a downward Löwenheim‐Skolem argument. Thus it is interesting to find a direct “elementary” proof. Here we show that this can be done.
FINITE REPLACEMENT AND FINITE HILBERT‐STYLE AXIOMATIZABILITY
Authors: Herrmann B. , Rautenberg W.
Published: May 2007

We define a property for varieties V, thef.r.p.(finite replacement property). If it applies to a finitely based V then V is strongly finitely based in the sense of [14], see Theorem 2. Moreover, we obtain finite axiomatizability results for certain propositional logics associated with V, in its generality comparable to well‐known finite base results from equational logic. Theorem 3 states that each variety generated by a 2‐element algebra has thef.r.p.Essentially this implies finite axiomatizability of a 2‐valued logic inany finitelanguage.
ALGEBRAIC CLOSURE WITHOUT CHOICE
Authors: Banaschewski Bernhard
Published: May 2007

This note shows that for the proof of the existence and uniqueness of the algebraic closure of a field one needs only the Boolean Ultrafilter Theorem.
A NOTATION SYSTEM FOR ORDINAL USING Ψ‐FUNCTIONS ON INACCESSIBLE MAHLO NUMBERS
Authors: Pfeiffer Helmut , Pfeiffer H.
Published: May 2007

G. Jäger gave in Arch. Math. Logik Grundlagenforsch. 24 (1984), 49‐62, a recursive notation system on a basis of a hierarchy Iαß of α‐inaccessible regular ordinals using collapsing functions following W. Buchholz in Ann. Pure Appl. Logic 32 (1986), 195‐207. Jäger's system stops, when ordinals α with Iα0 = α enter. This border is now overcome by introducing additional a hierarchy Jαß of weakly inaccessible Mahlo numbers, which is defined similarly to the Jäger hierarchy. An ordinal μ is called Mahlo, if every normal‐function f : μ → μ has regular fixpoints. Collapsing is defined for both Mahlo and simply regular ordinals such that for every Mahlo ordinal μ out of the J‐hierarchy Ψμα is a regular σ such that Iσ0 = σ. For these regular σ again collapsing functions Ψσ are defined. To get a proper systematical order into the collapsing procedure, a pair of ordinals is associated to σ and α, and the definition of Ψσα is given by recursion on a suitable well‐ordering of these pairs. Thus a fairly large system of ordinal notations can be established. It seems rather straightforward, how to extend this setting further.
QUANTIFIED MODAL LOGIC WITH NEIGHBORHOOD SEMANTICS
Authors: Waagbø Geir , Waagbø G.
Published: May 2007

The paper presents a semantics for quantified modal logic which has a weaker axiomatization than the usual Kripke semantics. In particular, the Barcan Formula (BF) and its converse are not valid with the proposed semantics. Subclasses of models which validate BF and other interesting formulas are presented. A completeness theorem is proved, and the relation between this result and completeness with respect to Kripke models is investigated.
More on the Least Strongly Compact Cardinal
Authors: Apter Arthur W.
Published: May 2007

We show that it is consistent, relative to a supercompact limit of supercompact cardinals, for the least strongly compact cardinal k to be both the least measurable cardinal and to be > 2k supercompact.
Extending Partial Orders on o‐Minimal Structures to Definable Total Orders
Authors: Macpherson Dugald , Steinhorn Charles
Published: May 2007

It is shown that if (M, <, ⃛) is an o‐minimal structure such that (M, <) is a dense total order and ≾ is a parameter‐definable partial order on M, then ≾ has an extension to a definable total order.
Association of matrix metalloproteinase‐2 and ‐9 promoter polymorphisms with colorectal cancer in Chinese
Authors: Xu Enping , Xia Xiaoping , Lü Bingjian , Xing Xiaoming , Huang Qiong , Ma Yu , Wang Wei , Lai Maode
Published: June 2007

Matrix metalloproteinase‐2 (MMP‐2) and ‐9 (MMP‐9) play an important role in cancer initiation, invasion, and metastasis. The aim of this study was to investigate whether common genetic variants in these two key MMPs are associated with the development and progression of colorectal cancer in a Chinese population. We detected the MMP‐2‐790T/G, ‐955A/C, ‐1575G/A, and MMP‐9‐1562 C/T polymorphisms in 126 colorectal cancer patients and matched normal controls by PCR‐denaturing high‐performance liquid chromatography (DHPLC) or PCR‐restriction fragment length polymorphism (RFLP), respectively. We found that the G/G genotype in the MMP‐2‐1575G/A polymorphism was significantly increased in colorectal cancer patients than in the controls (odds ratio (OR), 1.96; 95% CI, 1.06–3.64). Colorectal cancers with G/G genotype were more common with serosa/adventitia layer involvement than those with G/A + A/A genotypes (P < 0.05). However, no significant differences were observed in distribution of the MMP‐2‐790T/G, ‐955A/C, and MMP‐9‐1562 C/T polymorphisms or haplotype of MMP‐2 SNPs between patients and controls. Our results suggest that the presence of ‐1575G allele in the MMP‐2 promoter region may be of significance in the assessment of colorectal cancer risk and invasive potential. © 2007 Wiley‐Liss, Inc.