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Two forbidden induced subgraphs and well-quasi-ordering
Discrete Mathematics, 2011 It is known that a class of graphs defined by a single forbidden induced subgraph G is well-quasi-ordered by the induced subgraph relation if and only if G is an induced subgraph of P(4).
Nicholas Korpelainen, Vadim V Lozin
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Heavy subgraph pairs for traceability of block-chains [PDF]
Discussiones Mathematicae Graph Theory, 2014 A graph is called traceable if it contains a Hamilton path, i.e., a path containing all its vertices. Let G be a graph on n vertices. We say that an induced subgraph of G is o−1-heavy if it contains two nonadjacent vertices which satisfy an Ore-type ...
Li Binlong +2 more
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Line Graphs and Forbidden Induced Subgraphs
Journal of Combinatorial Theory, Series B, 2001 Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, Šoltés gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases.
Lai, Hong-Jian, Šoltés, Ľubomír
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A forbidden subgraph characterization of line-polar bipartite graphs
Discrete Applied Mathematics, 2010 A graph is polar if the vertex set can be partitioned into A and B in such a way that the subgraph induced by A is a complete multipartite graph and the subgraph induced by B is a disjoint union of cliques.
Jing Huang, Baogang Xu
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A forbidden induced subgraph characterization of distance-hereditary 5-leaf powers
Discrete Mathematics, 2009 A graph G is a k-leaf power if there is a tree T such that the vertices of G are the leaves of T and two vertices are adjacent in G if and only if their distance in T is at most k. In this situation T is called a k-leaf root of G. Motivated by the search
Andreas Brandstädt +2 more
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Reconfiguration of vertex colouring and forbidden induced subgraphs
European Journal of Combinatorics, 2023 The reconfiguration graph of the $k$-colourings, denoted $\mathcal{R}_k(G)$, is the graph whose vertices are the $k$-colourings of $G$ and two colourings are adjacent in $\mathcal{R}_k(G)$ if they differ in colour on exactly one vertex. In this paper, we
Merkel, Owen +2 more
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The largest subgraph without a forbidden induced subgraph
CombinatoricaWe initiate the systematic study of the following Tur\'an-type question. Suppose $\Gamma$ is a graph with $n$ vertices such that the edge density between any pair of subsets of vertices of size at least $t$ is at most $1 - c$, for some $t$ and $c > 0 ...
Pham, Huy Tuan +2 more
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Near-complete multipartite graphs and forbidden induced subgraphs
Discrete Mathematics, 1999 A proper vertex k-coloring C1,C2,…,Ck of a graph G is called l-bounded (l⩾0) if |Ci⧹N(u)|⩽l for each i=1,2,…,k and each vertex u∈VG⧹Ci, where N(u) is the neighborhood of u. Let C(k,l) be the class of all graphs having an l-bounded k-coloring (k⩾1 and l⩾0)
Zverovich, Igor E.
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On characterizing game-perfect graphs by forbidden induced subgraphs
Contributions to Discrete Mathematics, 2012 A graph $G$ is called $g$-perfect if, for any induced subgraph $H$ of $G$, the game chromatic number of $H$ equals the clique number of $H$. A graph $G$ is called $g$-col-perfect if, for any induced subgraph $H$ of $G$, the game coloring number of $H ...
Andres, Stephan Dominique
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Complexity Dichotomy for List-5-Coloring with a Forbidden Induced Subgraph [PDF]
SIAM Journal on Discrete Mathematics, 2022 First Published in the Journal of Discrete Mathematics in Volume 36, Issue 3, 2022, published by the Society for Industrial and Applied Mathematics (SIAM). Copyright © by SIAM.
Spirkl, Sophie +2 more
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