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The Ryjáček Closure and a Forbidden Subgraph
Discussiones Mathematicae Graph Theory, 2016 The Ryjáček closure is a powerful tool in the study of Hamiltonian properties of claw-free graphs. Because of its usefulness, we may hope to use it in the classes of graphs defined by another forbidden subgraph. In this note, we give a negative answer to
Saito Akira, Xiong Liming
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Forbidden subgraph pairs for traceability of block-chains
Electronic Journal of Graph Theory and Applications, 2013 A block-chain is a graph whose block graph is a path, i.e. it is either a $P_1$, a $P_2$, or a 2-connected graph, or a graph of connectivity 1 with exactly two end-blocks. A graph is called traceable if it contains a Hamilton path.
Binlong Li +2 more
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Characterising and recognising game-perfect graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours.
Dominique Andres, Edwin Lock
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The maximum spectral radius of graphs of given size with forbidden subgraph [PDF]
Linear Algebra and its Applications, 2022 Let $G$ be a graph of size $m$ and $\rho(G)$ be the spectral radius of its adjacency matrix. A graph is said to be $F$-free if it does not contain a subgraph isomorphic to $F$. In this paper, we prove that if $G$ is a $K_{2,r+1}$-free non-star graph with
Xiaona Fang, L. You
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List-3-Coloring Ordered Graphs with a Forbidden Induced Subgraph [PDF]
SIAM Journal on Discrete Mathematics, 2022 The List-3-Coloring Problem is to decide, given a graph $G$ and a list $L(v)\subseteq \{1,2,3\}$ of colors assigned to each vertex $v$ of $G$, whether $G$ admits a proper coloring $\phi$ with $\phi(v)\in L(v)$ for every vertex $v$ of $G$, and the $3 ...
Sepehr Hajebi, Yanjia Li, S. Spirkl
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Complexity Dichotomy for List-5-Coloring with a Forbidden Induced Subgraph [PDF]
SIAM Journal on Discrete Mathematics, 2021 For a positive integer $r$ and graphs $G$ and $H$, we denote by $G+H$ the disjoint union of $G$ and $H$, and by $rH$ the union of $r$ mutually disjoint copies of $H$. Also, we say $G$ is $H$-free if $H$ is not isomorphic to an induced subgraph of $G$. We
Sepehr Hajebi, Yanjia Li, S. Spirkl
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Clique minors in graphs with a forbidden subgraph [PDF]
Random Struct. Algorithms, 2020 The classical Hadwiger conjecture dating back to 1940s states that any graph of chromatic number at least r has the clique of order r as a minor. Hadwiger's conjecture is an example of a well‐studied class of problems asking how large a clique minor one ...
Matija Bucic, J. Fox, B. Sudakov
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Forbidden induced subgraph characterization of circle graphs within split graphs [PDF]
Discrete Applied Mathematics, 2020 A graph is circle if its vertices are in correspondence with a family of chords in a circle in such a way that every two distinct vertices are adjacent if and only if the corresponding chords have nonempty intersection.
Flavia Bonomo-Braberman +3 more
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Forbidden Subgraphs for Existences of (Connected) 2-Factors of a Graph
Discussiones Mathematicae Graph Theory, 2023 Clearly, having a 2-factor in a graph is a necessary condition for a graph to be hamiltonian, while having an even factor in graph is a necessary condition for a graph to have a 2-factor.
Yang Xiaojing, Xiong Liming
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Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition [PDF]
Electronic Journal of Combinatorics, 2016 Forbidden characterizations may sometimes be the most natural way to describe families of graphs, and yet these characterizations are usually very hard to exploit for enumerative purposes.By building on the work of Gioan and Paul (2012) and Chauve et al.(
Maryam Bahrani, Jérémie O. Lumbroso
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