bluuebunny/crossref_metadata_2025_split huggingface dataset:
Quantitative polymerase chain reaction as a reliable method to determine functional lentiviral titer after ex vivo gene transfer in human mesenchymal stem cells
Authors: Böcker Wolfgang , Rossmann Oliver , Docheva Denitsa , Malterer Georg , Mutschler Wolf , Schieker Matthias 
Published: May 2007

AbstractBackgroundHuman mesenchymal stem cells (hMSCs) are a promising target for ex vivo gene therapy and lentiviruses are excellent gene transfer vehicles in hMSCs since they achieve high transduction rates with long‐term gene expression. Nevertheless, senescence of hMSCs may limit therapeutic applications due to time‐consuming cell selection and viral titration. Here, we describe a fast and reliable method to determine functional lentiviral titer by quantitative polymerase chain reaction (qPCR) after highly efficient ex vivo gene transfer in hMSCs.MethodsLentivirus production was tested with different types of packaging systems. Using p24 ELISA remaining viral particles were detected in the cell culture supernatant. The lentiviral gene transfer efficiency was quantified by FACS analysis. Lentiviral titers were determined by qPCR of expressed transgenes.ResultsThird‐generation self‐inactivating vectors showed highly efficient gene transfer in hMSCs. No viral antigen was detected in the cell culture supernatant after four media changes, suggesting the absence of infectious particles after 4 days. We observed a linear correlation between virus dilution and level of transgene expression by qPCR analysis, therefore allowing viral titering by quantification of transgene expression. Finally, we demonstrated that transduced hMSCs retained their stem cell character by differentiation towards adipogenic, osteogenic and chondrogenic lineages.ConclusionsQuantification of transgene copy numbers by qPCR is a fast and reliable method to determine functional lentiviral titer after ex vivo gene transfer in hMSCs. Copyright © 2007 John Wiley & Sons, Ltd.
G‐CSF‐lentivirus administration in rats provided sustained elevated neutrophil counts and subsequent EPO‐lentivirus administration increased hematocrits
Authors: Brzezinski Margaret , Yanay Ofer , Waldron Lanaya , Barry Simon C. , Osborne William R. A. 
Published: May 2007

AbstractBackgroundTowards gene therapy treatment of patients with neutropenia, characterized by neutrophil counts < 500 cells/µl, we investigated the ability of lentivirus vectors to provide sustained granulocyte colony‐stimulating factor (G‐CSF) delivery and to permit transgene expression from a second virus administration in a preclinical rat model.MethodsRats were injected intramuscularly (IM) with 24 × 106 and 9 × 106 infectious units (IU) of a VSV‐G‐pseudotyped self‐inactivating (SIN) lentivirus encoding rat G‐CSF cDNA and containing cPPT and PRE elements. To determine the effectiveness of a second virus administration treated rats and a naïve rat received erythropoietin (EPO)‐lentivirus IM. Rats were monitored for neutrophil and red blood cell production. Lentivirus antibodies were assayed by virus‐neutralizing assay and ELISA.ResultsHigh and low dose virus administration increased neutrophil counts to 5660 ± 930 cells/µl (mean ± SD) and 4010 ± 850 cells/µl, respectively, that were sustained for > 17 months and were significantly higher than controls counts of 1890 ± 570 cells/µl (p⩽0.0002). Rats treated with EPO‐virus produced significantly increased hematocrits (HCT) (63.1 ± 4.3% vs. 46.0 ± 3.2%, p < 0.0001) without effect on G‐CSF‐virus‐mediated neutrophil production. Antivirus antibodies were not detectable at serum dilutions ≥1:10 by virus neutralization or ELISA. Lymphocytes and platelets were not significantly different between control and treated animals (p > 0.1). Only genomic DNA from muscle at injection sites was positive for provirus suggesting lack of virus spread.ConclusionsG‐CSF‐lentivirus administered IM provided elevated, sustained neutrophil counts that were unchanged by subsequent EPO‐lentivirus administration. Significantly increased hematocrits were obtained following EPO‐lentivirus delivery. These data support the treatment of patients with severe chronic neutropenia by dosed lentivirus delivery IM. Copyright © 2007 John Wiley & Sons, Ltd.
Some sufficient conditions for the existence of a 1‐factor
Authors: Nebeský Ladislav 
Published: May 2007

AbstractThe following theorem is proved: Let G be a graph of even order. Assume that there exists a connected spanning subgraph F of G such that for every set U of four vertices in G, if the subgraph of F induced by U is a star, then the subgraph of G induced by U is complete. Then G has a 1‐factor. The above theorem is derived from another sufficient condition for the existence of a 1‐factor, which is also proved in this paper (Lemma 1).
Counterexamples to two conjectures of Hilton
Authors: Fiorini S. 
Published: May 2007

AbstractCounterexamples are presented to the following two conjectures of Hilton:

A graph which does not contain a spanning K1t is Vl‐critical if and only if it is VC‐critical.
If G is a class‐two graph which contains a spanning Pl‐critical subgraph H of the same chromatic index as G, then G is Vl‐critical.
The counterexample to the second conjecture also illustrates that a class‐two graph can have distinct Pl‐critical subgraphs.
The embeddings of a graph—A survey
Authors: Stahl Saul 
Published: May 2007

AbstractTopological graph theory seeks to find answers to the question of how graphs map into surfaces. This paper surveys the information now available about the range of a graph, namely, the set of surfaces on which the graph can be “neatly” embedded. Several other closely related topics, such as irreducible graphs, coloring problems, and crossing numbers, are ignored. As is quite often the case with mathematical theories, this discipline developed in a rather haphazard manner. Many isolated results existed before the practitioners became aware of the fact that they were developing a theory. The turning point occurred in 1968, when Ringel and Youngs completed their proof of the Heawood conjecture. Their proof, in addition to settling an old unsolved problem, also reinforced the significance of the rotation systems. It is the author's belief that these rotation systems, together with the generalized embedding schemes can, and should, become the main tool in all investigations concerning the embeddings of a graph. This survey is written from that point of view. After defining the scope of the area surveyed, this paper proceeds to discuss the significance of the rotation systems and embedding schemes. Several theorems of a general nature are listed. Attention is then focused on the maximum and minimum genera of a graph. Discussion of the first of these is deferred to another survey article by R. Ringeisen to appear in a subsequent issue. The various methods developed by researchers in this area for determining the (minimum) genus are then described. This is followed by a listing of all the theoretical information that is available about the genus parameter. The paper includes two tables that exhibit most of the graphs with known genus.
The number of connected sparsely edged graphs. II. Smooth graphs and blocks
Authors: Wright E. M. 
Published: May 2007

AbstractA smooth graph is a connected graph without endpoints; f(n, q) is the number of connected graphs, v(n, q) is the number of smooth graphs, and u(n, q) is the number of blocks on n labeled points and q edges: Wk, Vk, and Uk are the exponential generating functions of f(n, n + k), v(n, n + k), and u(n, n + k), respectively. For any k ⩾ 1, our reduction method shows that Vk can be deduced at once from Wk, which was found for successive k by the computer method described in our previous paper. Again the reduction method shows that Uk must be a sum of powers (mostly negative) of 1 ‐ X and, given this information, we develop a recurrence method well suited to calculate Uk for successive k. Exact formulas for v(n, n + k) and u(n, n + k) for general n follow at once.
On the connectivity of maximal planar graphs
Authors: Hakimi S. L. , Schmeichel E. F. 
Published: May 2007

AbstractLet d1 ⩾ d2 ⩾ … ⩾ dp be the vertex degrees of a maximal planar graph G. Etourneau has shown that if d1 ⩽ 6 and dp = 5, then G is 5‐connected. We generalize Etourneau's result by giving sufficient conditions in terms of the vertex degrees for G to be dp ‐connected.
Characterization of maximum critically 2‐connected graphs
Authors: Entringer R. C. 
Published: May 2007

AbstractA graph G is critically 2‐connected if G is 2‐connected but, for any point p of G, G — p is not 2‐connected. Critically 2‐connected graphs on n points that have the maximum number of lines are characterized and shown to be unique for n ⩾ 3, n ≠ 11.
Graphs with symmetric automorphism group
Authors: Wallis W. D. , Heinrich Katherine 
Published: May 2007

AbstractWe investigate the properties of graphs whose automorphism group is the symmetric group. In particular, we characterize graphs on less than 2n points with group Sn, and construct all graphs on n + 3 points with group Sn. Graphs with 2n or more points and group Sn are discussed briefly.
1‐Factorizations of cartesian products of regular graphs
Authors: Kotzig Anton 
Published: May 2007

AbstractLet G1, G2…, Gn be regular graphs and H be the Cartesian product of these graphs (H = G1 × G2 × … × Gn). The following will be proved: If the set {G1, G2…, Gn} has at leat one of the following properties: (*) for at leat one i ϵ {1, 2,…, n}, there exists a 1‐factorization of Gi or (**) there exists at least two numbers i and j such that 1 ≤ i < j ≤ n and both the Graphs Gi and Gj contain at least one 1‐factor, then there exists a 1‐factorization of H. Further results: Let F be a cycle of length greater than three and let G be an arbitrary cubic graph. Then there exists a 1‐factorization of the 5‐regular graph H = F × G. The last result shows that neither (*) nor (**) is a necessary condition for the existence of a 1‐factorization of a Cartesian product of regular graphs.
An intermediate value theorem for graphs with given automorphism group
Authors: Hell Pavol , Quintas Louis V. 
Published: May 2007

AbstractFor a positive integer n and a finite group G, let the symbols e(G, n) and E(G, n) denote, respectively, the smallest and the greatest number of lines among all n‐point graphs with automorphism group G. We say that the Intermediate Value Theorem (IVT) holds for G and n, if for each e satisfying e(G, n)≤e≤E(G, n), there exists an n‐point graph with group G and e lines. The main result of this paper states that for every group G the IVT holds for all sufficiently large n. We also prove that the IVT holds for the identity group and all n, and exhibit examples of groups for which the IVT fails to hold for small values of n.
Cochromatic Number and the Genus of a Graph
Authors: Straight H. Joseph 
Published: May 2007

AbstractThe cochromatic number of a graph G, denoted by z(G), is the minimum number of subsets into which the vertex set of G can be partitioned so that each sbuset induces an empty or a complete subgraph of G. In this paper we introduce the problem of determining for a surface S, z(S), which is the maximum cochromatic number among all graphs G that embed in S. Some general bounds are obtained; for example, it is shown that if S is orientable of genus at least one, or if S is nonorientable of genus at least four, then z(S) is nonorientable of genus at least four, then z(S)≤χ(S). Here χ(S) denotes the chromatic number S. Exact results are obtained for the sphere, the Klein bottle, and for S. It is conjectured that z(S) is equal to the maximum n for which the graph Gn = K1 ∪ K2 ∪ … ∪ Kn embeds in S.
Voltage graph embeddings and the associated block designs
Authors: Garman Brian L. 
Published: May 2007

AbstractThe voltage graph construction of Gross (orientable case) and Stahl as well as Gross and Tucker (nonorientable case) is extended to the case where the base graph is embedded in a pseudosurface or a generalized pseudosurface. This theory is then applied to produce triangular embeddings of K4(n); they in turn yield an infinite class of partially balanced incomplete block designs.
Further annotated bibliography on the isomorphism disease
Authors: Gati Georg 
Published: May 2007

AbstractThis annotated bibliography contains 32 papers on graph isomorphism not included in the bibliography of Read and Corneil, most of which discuss algorithms or their theoretical foundations. We include articles by Miller, Weisfeiler, and Whitney as well as algorithms by Johnson and Leighton, Schmidt and Druffel, Tinhofer, and Erdös and Babai.
On the construction of the self‐complementary graphs on 12 nodes
Authors: Kropar Marg , Read Ronald C. 
Published: May 2007

AbstractWe briefly describe how we compiled a catalog of all the 720 self‐complementary graphs on 12 nodes. In our first attempt at this compilation one graph was inadvertently omitted. The missing graph was subsequently found by making use of a theoretical formula due to Parthasarathy and Sridharan for counting self‐complementary graphs with given partitions.
Group labelings of graphs
Authors: Edelman Paul H. , Saks Michael 
Published: May 2007

AbstractGiven a graph Γ an abelian group G, and a labeling of the vertices of Γ with elements of G, necessary and sufficient conditions are stated for the existence of a labeling of the edges in which the label of each vertex equals the product of the labels of its incident edges. Such an edge labeling is called compatible. For vertex labelings satisfying these conditions, the set of compatible edge labelings is enumerated.
Spanning arborescences, ingraphs, and outgraphs
Authors: Berman Kenneth A. 
Published: May 2007

AbstractAn ingraph N is a subgraph of a digraph G whose edge set consists of all the edges of G that are directed into a subset X of the vertices. Set X is the generating set of N. It is proved that G contains a unique even ingraph and this ingraph is generated by the set A of vertices that root an odd number of spanning out arborescences provided A is nonempty. If A is empty, then there exist at least two even ingraphs.
Graph‐theoretic characterization of the matrix property of full irreducibility without using a transversal
Authors: Kevorkian Aram K. 
Published: May 2007

AbstractIn this paper we introduce the notion of strongly connected polygons in the line graph of a bipartite graph. We use this notion to give a necessary and sufficient condition for a matrix Y to be fully irreducible without the need to construct a transversal of Y. In addition, we show that the notion of strongly connected polygons forms the basis of a general theory that may be used for finding all the cycles in the directed graph of a fully irreducible matrix and for constructing all the nonzero transversals of a fully irreducible matrix.
Orderly algorithms for generating restricted classes of graphs
Authors: Colbourn Charles J. , Read Ronald C. 
Published: May 2007

AbstractOrderly algorithms for the generation of exhaustive lists of nonisomorphic graphs are discussed. The existence of orderly methods to generate the graphs with a given subgraph and without a given subgraph is established. This method can be used to list all the nonisomorphic subgraphs of a given graph, as well as to produce catalogs of Hamiltonian graphs, pancyclic graphs, degree‐constrained graphs, and other classes. A generalization of this method is given that can be used to generate lists of graphs with given girth, planar graphs, k‐colorable graphs, and k‐connected graphs, for example. Finally, these observations are employed to generate restricted classes of digraphs, notably acyclic digraphs and poset digraphs. The generation of poset digraphs is shown to supply a practical orderly method for producing a catalog of lattices. Similar observations concerning vertex addition generation methods allow one to improve on existing methods for the generation of catalog of interval and circle graphs.
On double and multiple interval graphs
Authors: Trotter William T. , Harary Frank 
Published: May 2007

AbstractIn this paper we discuss a generalization of the familiar concept of an interval graph that arises naturally in scheduling and allocation problems. We define the interval number of a graph G to be the smallest positive integer t for which there exists a function f which assigns to each vertex u of G a subset f(u) of the real line so that f(u) is the union of t closed intervals of the real line, and distinct vertices u and v in G are adjacent if and only if f(u) and f(v)meet. We show that (1) the interval number of a tree is at most two, and (2) the complete bipartite graph Km, n has interval number ⌈(mn + 1)/(m + n)⌉.
On minimal strong blocks
Authors: Grötschel Martin 
Published: May 2007

AbstractIt is shown that storng blocks, i.e., digraphs that are strongly connected and have no cutnodes have an ear‐decomposition. This result is used to prove that the number q of arcs of minimal strong blocks is bounded by p ≤ q ≤ 2p – 3 and that minimal strong blocks contain at least two nodes with indegree and outdegree equal to one.
Properties of almost all graphs and complexes
Authors: Blass Andreas , Harary Frank 
Published: May 2007

AbstractThere are many results in the literature asserting that almost all or almost no graphs have some property. Our object is to develop a general logical theorem that will imply almost all of these results as corollaries. To this end, we propose the first‐order theory of almost all graphs by presenting Axiom n which states that for each sequence of 2n distinct vertices in a graph (u1, …, un, v1, …, vn), there exists another vertex w adjacent to each u1 and not adjacent to any vi. A simple counting argument proves that for each n, almost all graphs satisfy Axiom n. It is then shown that any sentence that can be stated in terms of these axioms is true in almost all graphs or in almost none. This has several immediate consequences, most of which have already been proved separately including: (1) For any graph H, almost all graphs have an induced subgraph isomorphic to H. (2) Almost no graphs are planar, or chordal, or line graphs. (3) Almost all grpahs are connected wiht diameter 2. It is also pointed out that these considerations extend to digraphs and to simplicial complexes.
Graph‐theoretic parameters concerning domination, independence, and irredundance
Authors: Bollobás B. , Cockayne E. J. 
Published: May 2007

AbstractA vertex x in a subset X of vertices of an undericted graph is redundant if its closed neighbourhood is contained in the union of closed neighborhoods of vertices of X – {x}. In the context of a communications network, this means that any vertex that may receive communications from X may also be informed from X – {x}. The irredundance number ir (G) is the minimum cardinality taken over all maximal sets of vertices having no redundancies. The domination number γ(G) is the minimum cardinality taken over all dominating sets of G, and the independent domination number i(G) is the minimum cardinality taken over all maximal independent sets of vertices of G. The paper contians results that relate these parameters. For example, we prove that for any graph G, ir (G) > γ(G)/2 and for any grpah Gwith p vertices and no isolated vertices, i(G) ≤ p‐γ(G) + 1 ‐ ⌈(p ‐ γ(G))/γ(G)⌉.
A sufficient condition for equality of edge‐connectivity and minimum degree of a graph
Authors: Goldsmith Donald L. , Entringer Roger C. 
Published: May 2007

AbstractLet G be a connected graph of order p ≥ 2, with edge‐connectivity κ1(G) and minimum degree δ(G). It is shown her ethat in order to obtain the equality κ1(G) = δ(G), it is sufficient that, for each vertex x of minimum degree in G, the vertices in the neighbourhood N(x) of x have sufficiently large degree sum. This result implies a previous result of Chartrand, which required that δ(G) ≥ [p/2].
Infinite families of biembedding numbers
Authors: Anderson I. 
Published: May 2007

AbstractLet N(γ, γ′) denote the size of the smallest complete graph that cannot be edge‐partitioned into two parts embeddable in closed orientable sufaces of genera γ, γ′, respectively. Well‐known embedding theorems are used to obtain several infinite families of values of N(γ, γ′). Some related small values of N(γ, γ′) are also discussed.
A class of self‐complementary graphs and lower bounds of some ramsey numbers
Authors: Clapham C. R. J. 
Published: May 2007

AbstractA method is described of constructing a class of self‐complementary graphs, that includes a self‐complementary graph, containing no K5, with 41 vertices and a self‐complementary graph, containing no K7, with 113 vertices. The latter construction gives the improved Ramsey number lower bound r(7, 7) ≥ 114.
Note on Choudum's “chromatic bounds for a class of graphs”
Authors: Javdekar Medha 
Published: May 2007

AbstractIf a graph G has no induced subgraph isomorphic to K1,3′ K5‐e, or a third graph that can be selected from two specific graphs, then the chromatic number of G is either d or d + 1, where d is the maximum order of a clique in G.
On the critical graph conjecture
Authors: Yap Hian Poh 
Published: May 2007

AbstractGol'dberg has recently constructed an infinite family of 3‐critical graphs of even order. We now prove that if there exists a p(≥4)‐critical graph K of odd order such that K has a vertex u of valency 2 and another vertex v ≠ u of valency ≤(p + 2)/2, then there exists a p‐critical graph of even order.
An upper bound on the length of a Hamiltonian walk of a maximal planar graph
Authors: Asano Takao , Nishizeki Takao , Watanabe Takahiro 
Published: May 2007

AbstractA Hamiltonian walk of a connected graph is a shortest closed walk that passes through every vertex at least once, and the length of a Hamiltonian walk is the total number of edges traversed by the walk. We show that every maximal planar graph with p(≥ 3) vertices has a Hamiltonian cycle or a Hamiltonian walk of length ≤ 3(p ‐ 3)/2.
On the Ramsey multiplicities of graphs—problems and recent results
Authors: Burr Stefan A. , Rosta Vera 
Published: May 2007

AbstractRamsey's theorem guarantees that if G is a graph, then any 2‐coloring of the edges of a large enough complete graph yields a monochromatic copy of G. Interesting problems arise when one asks how many such G must occur. A survey of this and related problems is given, along with a number of new results.
The chromatic index of graphs with a spanning star
Authors: Plantholt Mike 
Published: May 2007

AbstractVizing's Theorem states that any graph G has chromatic index either the maximum degree Δ(G) or Δ(G) + 1. If G has 2s + 1 points and Δ(G) = 2s, a well‐known necessary condition for the chromatic index to equal 2s is that G have at most 2s2 lines. Hilton conjectured that this condition is also sufficient. We present a proof of that conjecture and a corollary that helps determine the chromatic index of some graphs with 2s points and maximum degree 2s − 2.
A duality theorem for graph embeddings
Authors: Jackson Brad , Parsons T. D. , Pisanski Tomaž 
Published: May 2007

AbstractA generalized type of graph covering, called a “Wrapped quasicovering” (wqc) is defined. If K, L are graphs dually embedded in an orientable surface S, then we may lift these embeddings to embeddings of dual graphs K̃,L̃ in orientable surfaces S̃, such that S̃ are branched covers of S and the restrictions of the branched coverings to K̃,L̃ are wqc's of K, L. the theory is applied to obtain genus embeddings of composition graphs G[nK1] from embeddings of “quotient” graphs G.
A graph and its complement with specified properties. IV. Counting self‐complementary blocks
Authors: Akiyama Jin , Harary Frank 
Published: May 2007

AbstractIn this series, we investigate the conditions under which both a graph G and its complement G possess certain specified properties. We now characterize all the graphs G such that both G and G have the same number of endpoints, and find that this number can only be 0 or 1 or 2. As a consequence, we are able to enumerate the self‐complementary blocks.