Results 31 to 40 of about 87,339 (166)
Chromatic number, clique subdivisions, and the conjectures of Haj\'os and Erd\H{o}s-Fajtlowicz [PDF]
, 2011 For a graph $G$, let $\chi(G)$ denote its chromatic number and $\sigma(G)$ denote the order of the largest clique subdivision in $G$. Let H(n) be the maximum of $\chi(G)/\sigma(G)$ over all $n$-vertex graphs $G$.
A. B. Kupavskii +17 more
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Anagram-Free Colorings of Graph Subdivisions
SIAM Journal on Discrete Mathematics, 2018 An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$ is a permutation of $W$. A vertex colouring of a graph is anagram-free if no subpath of the graph is an anagram. Anagram-free graph colouring was independently introduced by Kam ev, uczak and Sudakov and ourselves.
Tim E. Wilson, David R. Wood
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Coined Quantum Walks as Quantum Markov Chains [PDF]
, 2017 We analyze the equivalence between discrete-time coined quantum walks and Szegedy's quantum walks. We characterize a class of flip-flop coined models with generalized Grover coin on a graph $\Gamma$ that can be directly converted into Szegedy's model on ...
Portugal, Renato, Segawa, Etsuo
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Odd K3,3 subdivisions in bipartite graphs
Journal of Combinatorial Theory, Series B, 2016 We prove that every internally 4-connected non-planar bipartite graph has an odd K_3,3 subdivision; that is, a subgraph obtained from K_3,3 by replacing its edges by internally disjoint odd paths with the same ends. The proof gives rise to a polynomial-time algorithm to find such a subdivision.
Thomas, Robin, Whalen, Peter
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Subdivisions in apex graphs [PDF]
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2012 The Kelmans-Seymour conjecture states that the 5-connected nonplanar graphs contain a subdivided $K_{_5}$. Certain questions of Mader propose a "plan" towards a possible resolution of this conjecture. One part of this plan is to show that a 5-connected nonplanar graph containing $K^-_{_4}$ or $K_{_{2,3}}$ as a subgraph has a subdivided $K_{_5 ...
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The nonsplit domination in subdivision graphs
Proyecciones (Antofagasta), 2020 A dominating set D of a graph G = (V, E) is a nonsplit dominating set if the induced subgraph 〈V − D〉 is connected. The nonsplit domination number γns(G) of G is the minimum cardinality of a nonsplit dominating set. An edge e = uv of a graph G is said to be subdivided if e is replaced by the edges uw and vw for some vertex w not in V (G).
R. Jemimal Chrislight +1 more
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Graph colorings and digraph subdivisions [PDF]
Anais do XXXI Concurso de Teses e Dissertações (CTD 2018), 2018 This paper presents our studies on three vertex coloring problems on graphs and on a problem concerning subdivision of digraphs. Given an arbitrarily colored graph G, the convex recoloring problem consists in finding a (re)coloring that minimizes the number of color changes and such that each color class induces a connected subgraph of G.
Phablo F. S. Moura, Yoshiko Wakabayashi
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The harmonic index of subdivision graphs [PDF]
Transactions on Combinatorics, 2017 The harmonic index of a graph $G$ is defined as the sum of the weights $frac{2}{deg_G(u)+deg_G(v)}$ of all edges $uv$ of $G$, where $deg_G(u)$ denotes the degree of a vertex $u$ in $G$. In this paper, we study the harmonic index of subdivision
Bibi Naimeh Onagh
doaj +1 more source
Topological minors of cover graphs and dimension [PDF]
, 2016 We show that posets of bounded height whose cover graphs exclude a fixed graph as a topological minor have bounded dimension. This result was already proven by Walczak.
Dujmović +16 more
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First reformulated Zagreb indices of some classes of graphs
Karpatsʹkì Matematičnì Publìkacìï, 2018 A topological index of a graph is a parameter related to the graph; it does not depend on labeling or pictorial representation of the graph. Graph operations plays a vital role to analyze the structure and properties of a large graph which is derived ...
V. Kaladevi +2 more
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