bluuebunny/crossref_metadata_2025_split huggingface dataset:
Vertex-Addition Strategy for Domination-Like Invariants
Authors: Furuya Michitaka , Matsumoto Naoki 
Published: January 2020

In [J. Graph Theory 13 (1989) 749—762], McCuaig and Shepherd gave an upper bound of the domination number for connected graphs with minimum degree at least two. In this paper, we propose a simple strategy which, together with the McCuaig-Shepherd theorem, gives a sharp upper bound of the domination number via the number of leaves. We also apply the same strategy to other domination-like invariants, and find a relationship between such invariants and the number of leaves.
Inversion Generating Functions for Signed Pattern Avoiding Permutations
Authors: Cameron Naiomi T. , Killpatrick Kendra 
Published: January 2020

We consider the classical Mahonian statistics on the set $B_n(\Sigma)$ of signed permutations in the hyperoctahedral group $B_n$ which avoid all patterns in $\Sigma$, where $\Sigma$ is a set of patterns of length two. In 2000, Simion gave the cardinality of $B_n(\Sigma)$ in the cases where $\Sigma$ contains either one or two patterns of length two and showed that $\left|B_n(\Sigma)\right|$ is constant whenever $\left|\Sigma\right|=1$, whereas in most but not all instances where $\left|\Sigma\right|=2$, $\left|B_n(\Sigma)\right|=(n+1)!$. We answer an open question of Simion by providing bijections from $B_n(\Sigma)$ to $S_{n+1}$ in these cases where $\left|B_n(\Sigma)\right|=(n+1)!$. In addition, we extend Simion's work by providing a combinatorial proof in the language of signed permutations for the major index on $B_n(21, \bar{2}\bar{1})$ and by giving the major index on $D_n(\Sigma)$ for $\Sigma =\{21, \bar{2}\bar{1}\}$ and $\Sigma=\{12,21\}$. The main result of this paper is to give the inversion generating functions for $B_n(\Sigma)$ for almost all sets $\Sigma$ with $\left|\Sigma\right|\leq2.$
Some Properties of the Fibonacci Sequence on an Infinite Alphabet
Authors: Zhang Jiemeng , Wen Zhixiong , Wu Wen 
Published: January 2020

The infinite Fibonacci sequence $\mathbf{F}$, which is an extension of the classic Fibonacci sequence to the infinite alphabet $\mathbb{N}$, is the fixed point of the morphism $\phi$: $(2i)\mapsto (2i)(2i+1)$ and $(2i+1)\mapsto (2i+2)$ for all $i\in\mathbb{N}$. In this paper, we study the growth order and digit sum of $\mathbf{F}$ and give several decompositions of $\mathbf{F}$ using singular words.
Extending Perfect Matchings to Gray Codes with Prescribed Ends
Authors: Gregor Petr , Novotný Tomáš , Škrekovski Riste 
Published: January 2020

A binary (cyclic) Gray code is a (cyclic) ordering of all binary strings of the same length such that any two consecutive strings differ in a single bit. This corresponds to a Hamiltonian path (cycle) in the hypercube. Fink showed that every perfect matching in the $n$-dimensional hypercube $Q_n$ can be extended to a Hamiltonian cycle, confirming a conjecture of Kreweras. In this paper, we study the "path version" of this problem. Namely, we characterize when a perfect matching in $Q_n$ extends to a Hamiltonian path between two prescribed vertices of opposite parity. Furthermore, we characterize when a perfect matching in $Q_n$ with two faulty vertices extends to a Hamiltonian cycle. In both cases we show that for all dimensions $n\ge 5$ the only forbidden configurations are so-called half-layers, which are certain natural obstacles. These results thus extend Kreweras' conjecture with an additional edge, or with two faulty vertices. The proof for the case $n=5$ is computer-assisted.
A Note on the Expected Length of the Longest Common Subsequences of two i.i.d. Random Permutations
Authors: Houdré Christian , Xu Chen 
Published: January 2020

We address a question and a conjecture on the expected length of the longest common subsequences of two i.i.d. random permutations of $[n]:=\{1,2,...,n\}$. The question is resolved by showing that the minimal expectation is not attained in the uniform case. The conjecture asserts that $\sqrt{n}$ is a lower bound on this expectation, but we only obtain $\sqrt[3]{n}$ for it.
Large Monochromatic Components in Edge Colored Graphs with a Minimum Degree Condition
Authors: Gyárfás András , Sárközy Gábor 
Published: January 2020

It is well-known that in every $k$-coloring of the edges of the complete graph $K_n$ there is a monochromatic connected component of order at least ${n\over k-1}$. In this paper we study an extension of this problem by replacing complete graphs by graphs of large minimum degree. For $k=2$ the authors proved that $\delta(G)\ge{3n\over 4}$ ensures a monochromatic connected component with at least $\delta(G)+1$ vertices in every $2$-coloring of the edges of a graph $G$ with $n$ vertices. This result is sharp, thus for $k=2$ we really need a complete graph to guarantee that one of the colors has a monochromatic connected spanning subgraph. Our main result here is that for larger values of $k$ the situation is different, graphs of minimum degree $(1-\epsilon_k)n$ can replace complete graphs and still there is a monochromatic connected component of order at least ${n\over k-1}$, in fact $$\delta(G)\ge \left(1 - \frac{1}{1000(k-1)^9}\right)n$$ suffices.Our second result is an improvement of this bound for $k=3$. If the edges of $G$ with $\delta(G)\geq {9n\over 10}$ are $3$-colored, then there is a monochromatic component of order at least ${n\over 2}$. We conjecture that this can be improved to ${7n\over 9}$ and for general $k$ we conjecture the following: if $k\geq 3$ and $G$ is a graph of order $n$ such that $\delta(G)\geq \left( 1 - \frac{k-1}{k^2}\right)n$, then in any $k$-coloring of the edges of $G$ there is a monochromatic connected component of order at least ${n\over k-1}$.
Some Variations on a Theme of Irina Mel'nichuk Concerning the Avoidability of Patterns in Strings of Symbols
Authors: McNulty George F. 
Published: January 2020

The set of all doubled patterns on $n$ or fewer letters can be avoided on an alphabet with $k$ letters, where $k$ is the least even integer strictly greater than $n+1$, with the exception of $n=4$. The set of all doubled patterns on $4$ or fewer letters can be avoided on the $8$-letter alphabet. The set of all avoidable patterns on $n$ or fewer letters can be avoided on an alphabet with $2(n+2)$ letters.
The Cycle Polynomial of a Permutation Group
Authors: Cameron Peter J. , Semeraro Jason 
Published: January 2020

The cycle polynomial of a finite permutation group $G$ is the generating function for the number of elements of $G$ with a given number of cycles:\[F_G(x) = \sum_{g\in G}x^{c(g)},\] where $c(g)$ is the number of cycles of $g$ on $\Omega$. In the first part of the paper, we develop basic properties of this polynomial, and give a number of examples. In the 1970s, Richard Stanley introduced the notion of reciprocity for pairs of combinatorial polynomials. We show that, in a considerable number of cases, there is a polynomial in the reciprocal relation to the cycle polynomial of $G$; this is the orbital chromatic polynomial of $\Gamma$ and $G$, where $\Gamma$ is a $G$-invariant graph, introduced by the first author, Jackson and Rudd. We pose the general problem of finding all such reciprocal pairs, and give a number of examples and characterisations: the latter include the cases where $\Gamma$ is a complete or null graph or a tree. The paper concludes with some comments on other polynomials associated with a permutation group.
A Note on the Linear Cycle Cover Conjecture of Gyárfás and Sárközy
Authors: Ergemlidze Beka , Győri Ervin , Methuku Abhishek 
Published: January 2020

A linear cycle in a $3$-uniform hypergraph $H$ is a cyclic sequence of hyperedges such that any two consecutive hyperedges intersect in exactly one element and non-consecutive hyperedges are disjoint. Let $\alpha(H)$ denote the size of a largest independent set of $H$.We show that the vertex set of every $3$-uniform hypergraph $H$ can be covered by at most $\alpha(H)$ edge-disjoint linear cycles (where we accept a vertex and a hyperedge as a linear cycle), proving a weaker version of a conjecture of Gyárfás and Sárközy.
An Orthosymplectic Pieri Rule
Authors: Stokke Anna 
Published: January 2020

The classical Pieri formula gives a combinatorial rule for decomposing the product of a Schur function and a complete homogeneous symmetric polynomial as a linear combination of Schur functions with integer coefficients. We give a Pieri rule for describing the product of an orthosymplectic character and an orthosymplectic character arising from a one-row partition. We establish that the orthosymplectic Pieri rule coincides with Sundaram's Pieri rule for symplectic characters and that orthosymplectic characters and symplectic characters obey the same product rule.
Defective and Clustered Graph Colouring
Authors: Wood David R. 
Published: January 2020

Consider the following two ways to colour the vertices of a graph where the requirement that adjacent vertices get distinct colours is relaxed. A colouring has defect $d$ if each monochromatic component has maximum degree at most $d$. A colouring has clustering $c$ if each monochromatic component has at most $c$ vertices. This paper surveys research on these types of colourings, where the first priority is to minimise the number of colours, with small defect or small clustering as a secondary goal. List colouring variants are also considered. The following graph classes are studied: outerplanar graphs, planar graphs, graphs embeddable in surfaces, graphs with given maximum degree, graphs with given maximum average degree, graphs excluding a given subgraph, graphs with linear crossing number, linklessly or knotlessly embeddable graphs, graphs with given Colin de Verdière parameter, graphs with given circumference, graphs excluding a given immersion, graphs with given thickness, graphs with given stack- or queue-number, graphs excluding $K_t$ as a minor, graphs excluding $K_{s,t}$ as a minor, and graphs excluding an arbitrary graph $H$ as a minor. Several open problems are discussed.
Centroidal Localization Game
Authors: Bosek Bartłomiej , Gordinowicz Przemysław , Grytczuk Jarosław , Nisse Nicolas , Sokół Joanna , Śleszyńska-Nowak Małgorzata 
Published: January 2020

One important problem in a network $G$ is to locate an (invisible) moving entity by using distance-detectors placed at strategical locations in $G$. For instance, the famous metric dimension of a graph $G$ is the minimum number $k$ of detectors placed in some vertices $\{v_1,\cdots,v_k\}$ such that the vector $(d_1,\cdots,d_k)$ of the distances $d(v_i,r)$ between the detectors and the entity's location $r$ allows to uniquely determine $r$ for every $r \in V(G)$. In a more realistic setting, each device does not get the exact distance to the entity's location. Rather, given locating devices placed in $\{v_1,\cdots,v_k\}$, we get only relative distances between the moving entity's location $r$ and the devices (roughly, for every $1\leq i,j\leq k$, it is provided whether $d(v_i,r) >$, $<$, or $=$ to $d(v_j,r)$). The centroidal dimension of a graph $G$ is the minimum number of devices required to locate the entity, in one step, in this setting.In this paper, we consider the natural generalization of the latter problem, where vertices may be probed sequentially (i.e., in several steps) until the moving entity is located. Roughly, at every turn, a set $\{v_1,\cdots,v_k\}$ of vertices are probed and then the relative order of the distances between the vertices $v_i$ and the current location $r$ of the moving entity is given. If it not located, the moving entity may move along one edge. Let $\zeta^* (G)$ be the minimum $k$ such that the entity is eventually located, whatever it does, in the graph $G$. We first prove that $\zeta^* (T)\leq 2$ for every tree $T$ and give an upper bound on $\zeta^*(G\square H)$ for the cartesian product of graphs $G$ and $H$. Our main result is that $\zeta^* (G)\leq 3$ for any outerplanar graph $G$. We then prove that $\zeta^* (G)$ is bounded by the pathwidth of $G$ plus 1 and that the optimization problem of determining $\zeta^* (G)$ is NP-hard in general graphs. Finally, we show that approximating (up to a small constant distance) the location of the robber in the Euclidean plane requires at most two vertices per turn.
Hultman Elements for the Hyperoctahedral Groups
Authors: Woo Alexander 
Published: January 2020

Hultman, Linusson, Shareshian, and Sjöstrand gave a pattern avoidance characterization of the permutations for which the number of chambers of its associated inversion arrangement is the same as the size of its lower interval in Bruhat order. Hultman later gave a characterization, valid for an arbitrary finite reflection group, in terms of distances in the Bruhat graph. On the other hand, the pattern avoidance criterion for permutations had earlier appeared in independent work of Sjöstrand and of Gasharov and Reiner. We give characterizations of the elements of the hyperoctahedral groups satisfying Hultman's criterion that is in the spirit of those of Sjöstrand and of Gasharov and Reiner. We also give a pattern avoidance criterion using the notion of pattern avoidance defined by Billey and Postnikov.
Vertically Constrained Motzkin-Like Paths Inspired by Bobbin Lace
Authors: Irvine Veronika , Melczer Stephen , Ruskey Frank 
Published: January 2020

Inspired by a new mathematical model for bobbin lace, this paper considers finite lattice paths formed from the set of step vectors $\mathfrak{A}=$$\{\rightarrow,$ $\nearrow,$ $\searrow,$ $\uparrow,$ $\downarrow\}$ with the restriction that vertical steps $(\uparrow, \downarrow)$ cannot be consecutive. The set $\mathfrak{A}$ is the union of the well known Motzkin step vectors $\mathfrak{M}=$$\{\rightarrow,$ $\nearrow,$ $\searrow\}$ with the vertical steps $\{\uparrow, \downarrow\}$. An explicit bijection $\phi$ between the exhaustive set of vertically constrained paths formed from $\mathfrak{A}$ and a bisection of the paths generated by $\mathfrak{M}S$ is presented. In a similar manner, paths with the step vectors $\mathfrak{B}=$$\{\nearrow,$ $\searrow,$ $\uparrow,$ $\downarrow\}$, the union of Dyck step vectors and constrained vertical steps, are examined. We show, using the same $\phi$ mapping, that there is a bijection between vertically constrained $\mathfrak{B}$ paths and the subset of Motzkin paths avoiding horizontal steps at even indices. Generating functions are derived to enumerate these vertically constrained, partially directed paths when restricted to the half and quarter-plane. Finally, we extend Schröder and Delannoy step sets in a similar manner and find a bijection between these paths and a subset of Schröder paths that are smooth (do not change direction) at a regular horizontal interval.
An Explicit Edge-Coloring of $K_n$ with Six Colors on Every $K_5$
Authors: Cameron Alex 
Published: January 2020

Let $p$ and $q$ be positive integers such that $1 \leq q \leq {p \choose 2}$. A $(p,q)$-coloring of the complete graph on $n$ vertices $K_n$ is an edge coloring for which every $p$-clique contains edges of at least $q$ distinct colors. We denote the minimum number of colors needed for such a $(p,q)$-coloring of $K_n$ by $f(n,p,q)$. This is known as the Erdös-Gyárfás function. In this paper we give an explicit $(5,6)$-coloring with $n^{1/2+o(1)}$ colors. This improves the best known upper bound of $f(n,5,6)=O\left(n^{3/5}\right)$ given by Erdös and Gyárfás, and comes close to matching the order of the best known lower bound, $f(n,5,6) = \Omega\left(n^{1/2}\right)$.
On the Subnet Prune and Regraft Distance
Authors: Klawitter Jonathan , Linz Simone 
Published: January 2020

Phylogenetic networks are rooted directed acyclic graphs that represent evolutionary relationships between species whose past includes reticulation events such as hybridisation and horizontal gene transfer. To search the space of phylogenetic networks, the popular tree rearrangement operation rooted subtree prune and regraft (rSPR) was recently generalised to phylogenetic networks. This new operation – called subnet prune and regraft (SNPR) – induces a metric on the space of all phylogenetic networks as well as on several widely-used network classes. In this paper, we investigate several problems that arise in the context of computing the SNPR-distance. For a phylogenetic tree $T$ and a phylogenetic network $N$, we show how this distance can be computed by considering the set of trees that are embedded in $N$ and then use this result to characterise the SNPR-distance between $T$ and $N$ in terms of agreement forests. Furthermore, we analyse properties of shortest SNPR-sequences between two phylogenetic networks $N$ and $N'$, and answer the question whether or not any of the classes of tree-child, reticulation-visible, or tree-based networks isometrically embeds into the class of all phylogenetic networks under SNPR.
Random Kneser Graphs and Hypergraphs
Authors: Kupavskii Andrey 
Published: January 2020

The Kneser graph $KG_{n,k}$ is the graph whose vertices are the $k$-element subsets of $[n],$ with two vertices adjacent if and only if the corresponding sets are disjoint. A famous result due to Lovász states that the chromatic number of $KG_{n,k}$ is equal to $n-2k+2$. In this paper we discuss the chromatic number of random Kneser graphs and hypergraphs. It was studied in two recent papers, one due to Kupavskii, who proposed the problem and studied the graph case, and the more recent one due to Alishahi and Hajiabolhassan. The authors of the latter paper had extended the result of Kupavskii to the case of general Kneser hypergraphs. Moreover, they have improved the bounds of Kupavskii in the graph case for many values of parameters.In the present paper we present a purely combinatorial approach to the problem based on blow-ups of graphs, which gives much better bounds on the chromatic number of random Kneser and Schrijver graphs and Kneser hypergraphs. This allows us to improve all known results on the topic. The most interesting improvements are obtained in the case of $r$-uniform Kneser hypergraphs with $r\ge 3$, where we managed to replace certain polynomial dependencies of the parameters by the logarithmic ones.
The Classification of $2$-Extendable Edge-Regular Graphs with Diameter $2$
Authors: Kutnar Klavdija , Marušič Dragan , Miklavič Štefko , Šparl Primož 
Published: January 2020

Let $\ell$ denote a non-negative integer. A connected graph $\Gamma$ of even order at least $2\ell+2$ is $\ell$-extendable if it contains a matching of size $\ell$ and if every such matching is contained in a perfect matching of $\Gamma$. A connected regular graph $\Gamma$ is edge-regular, if there exists an integer $\lambda$ such that every pair of adjacent vertices of $\Gamma$ have exactly $\lambda$ common neighbours. In this paper we classify $2$-extendable edge-regular graphs of even order and diameter $2$.
Saturation Games for Odd Cycles
Authors: Spiro Sam 
Published: January 2020

Given a family of graphs $\mathcal{F}$, we consider the $\mathcal{F}$-saturation game. In this game, two players alternate adding edges to an initially empty graph on $n$ vertices, with the only constraint being that neither player can add an edge that creates a subgraph that lies in $\mathcal{F}$. The game ends when no more edges can be added to the graph. One of the players wishes to end the game as quickly as possible, while the other wishes to prolong the game. We let $\textrm{sat}_g(\mathcal{F};n)$ denote the number of edges that are in the final graph when both players play optimally.
The $\{C_3\}$-saturation game was the first saturation game to be considered, but as of now the order of magnitude of $\textrm{sat}_g(\{C_3\},n)$ remains unknown. We consider a variation of this game. Let $\mathcal{C}_{2k+1}:=\{C_3,\ C_5,\ldots,C_{2k+1}\}$. We prove that $\textrm{sat}_g(\mathcal{C}_{2k+1};n)\ge(\frac{1}{4}-\epsilon_k)n^2+o(n^2)$ for all $k\ge 2$ and that $\textrm{sat}_g(\mathcal{C}_{2k+1};n)\le (\frac{1}{4}-\epsilon'_k)n^2+o(n^2)$ for all $k\ge 4$, with $\epsilon_k<\frac{1}{4}$ and $\epsilon'_k>0$ constants tending to 0 as $k\to \infty$. In addition to this we prove $\textrm{sat}_g(\{C_{2k+1}\};n)\le \frac{4}{27}n^2+o(n^2)$ for all $k\ge 2$, and $\textrm{sat}_g(\mathcal{C}_\infty\setminus C_3;n)\le 2n-2$, where $\mathcal{C}_\infty$ denotes the set of all odd cycles.
On a Positivity Conjecture in the Character Table of $S_n$
Authors: Sundaram Sheila 
Published: January 2020

In previous work of this author it was conjectured that the sum of power sums $p_\lambda,$ for partitions $\lambda$ ranging over an interval $[(1^n), \mu]$ in reverse lexicographic order, is Schur-positive. Here we investigate this conjecture and establish its truth in the following special cases: for $\mu\in [(n-4,1^4), (n)]$ or $\mu\in [(1^n), (3,1^{n-3})], $ or $\mu=(3, 2^k, 1^r)$ when $k\geq 1$ and $0\leq r\leq 2.$ Many new Schur positivity questions are presented.
Des revendications ordinaires aux mobilisations citoyennes : la conquête du droit à la ville dans des quartiers informels de Batna (Algérie)
Authors: Belmessous Fatiha , Naceur Farida 
Published: January 2020

Cet article vise à comprendre comment au sein du système semi-autoritaire algérien émergent diverses formes de mobilisation, qu’elles traduisent une volonté d’accéder aux nécessaires ressources urbaines ou de participer à la vie politique locale. Pour l’illustrer, nous avons choisi de présenter la construction de légitimités citoyennes à la suite de différents récits, individuels et collectifs, dans une ville moyenne de l’Est algérien (la ville de Batna) au sein de quartiers non réglementaires. Le choix des quartiers informels (c’est-à-dire conçus en dehors de la planification et de la réglementation) comme cadre d’analyse de ces mobilisations citoyennes s’explique par la dynamique et la capacité de revendication de leurs résidents pour l’amélioration de leur vie quotidienne. Ce qui nous intéresse particulièrement est d’analyser le passage de revendications localisées à la construction de véritables légitimités, et par-là, à la reconnaissance de ces habitants comme des citoyens ordinaires au sein de la ville (en dépit du caractère informel de leurs lieux de vie). Comment les populations de ces quartiers parviennent-elles à développer une capacité d’organisation et de mobilisation pour construire leur propre légitimité ? Comment interagissent-elles avec les sphères du pouvoir alors qu’elles vivent en dehors de la légalité juridique ?
Simone de Beauvoir — La Pléiade
Authors: Le Bon de Beauvoir Sylvie , Jeannelle Jean-Louis , Adler Laure 
Published: January 2020

L’entretien est centré sur la sortie en mai 2018 des Mémoires de Simone de Beauvoir, deux tomes accompagnés d’un album biographique illustré, dans la Bibliothèque de la Pléiade (éditions Gallimard). Il évoque la personne, l’œuvre littéraire et la pensée de Simone de Beauvoir à la fois à partir du témoignage vécu de sa fille adoptive Sylvie Le Bon de Beauvoir et de l’approche universitaire de Jean-Louis Jeannelle.
Le Deuxième sexe
Authors: Le Bon de Beauvoir Sylvie 
Published: January 2020

On constate, 26 ans après la parution du Deuxième sexe , l’extension mondiale du féminisme. Cependant la pensée de l’œuvre, que résume la formule explosive « On ne naît pas femme, on le devient », est souvent déformée. L’article en rappelle le sens : aucune essence, aucune nature, aucun destin ne définit l’être des femmes, mais pour qu’elles accèdent à la libre existence, une lutte, tant individuelle que collective, est nécessaire.
Une nouvelle traduction du Deuxième sexe
Authors: Borde Constance , Malovany-Chevallier Sheila 
Published: January 2020

La nouvelle et tant attendue traduction anglaise du Deuxième sexe fut publiée en 2009. La traduction de la phrase « One is not born, but rather becomes, woman » (dont on supprime l’article indéfini « a » devant « woman ») apporte un nouveau regard sur le sens du texte. Chaque mot résulte d’un choix qui restituera fidèlement la voix et les idées de Beauvoir.