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Eigenvalues and forbidden subgraphs I
Linear Algebra and its Applications, 2006 Some calculation errors in the first version are ...
Vladimir Nikiforov
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Forbidden Induced Subgraphs [PDF]
Electronic Notes in Discrete Mathematics, 2017 In descending generality I survey: five partial orderings of graphs, the induced-subgraph ordering, and examples like perfect, threshold, and mock threshold graphs. The emphasis is on how the induced subgraph ordering differs from other popular orderings and leads to different basic questions.
Thomas Zasĺavsky
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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 subgraphs in the norm graph
Discrete Mathematics, 2015 We show that the norm graph constructed in [J. Koll r, L. R nyai and T. Szab , Norm-graphs and bipartite Tur n numbers, Combinatorica, 16 (1996) 399--406] with $n$ vertices about $\frac{1}{2}n^{2-1/t}$ edges, which contains no copy of $K_{t,(t-1)!+1}$, does not contain a copy of $K_{t+1,(t-1)!-1}$.
Simeon Ball, Valentina Pepe
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Disjoint stars and forbidden subgraphs
Hiroshima Mathematical Journal, 2006 Let $r,k$ be integers with $r\ge 3, k\ge 2$. We prove that if $G$ is a $K_{1,r}$-free graph of order at least $(k-1)(2r-1)+1$ with $\delta(G)\ge 2$, then $G$ contains $k$ vertex-disjoint copies of $K_{1,2}$. This result is motivated by the problem of characterizing a forbidden subgraph $H$ which satisfies the statement "every $H$-free graph of ...
Shinya Fujita
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Forbidden subgraphs of coloring graphs [PDF]
Involve, a Journal of Mathematics, 2017 Given a graph G, its k-coloring graph has vertex set given by the proper k-colorings of the vertices of G with two k-colorings adjacent if and only if they differ at exactly one vertex. Beier et al. (Discrete Math. 339:8 (2016), 2100–2112) give various characterizations of coloring graphs, including finding graphs which never arise as induced subgraphs
Francisco Alvarado +3 more
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Toughness, Forbidden Subgraphs, and Hamilton-Connected Graphs
Discussiones Mathematicae Graph Theory, 2022 A graph G is called Hamilton-connected if for every pair of distinct vertices {u, v} of G there exists a Hamilton path in G that connects u and v. A graph G is said to be t-tough if t·ω(G − X) ≤ |X| for all X ⊆ V (G) with ω(G − X) > 1. The toughness of G,
Zheng Wei, Broersma Hajo, Wang Ligong
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A pair of forbidden subgraphs and perfect matchings
Journal of Combinatorial Theory, Series B, 2005 AbstractIn this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to be H-free if no graph in H is an induced subgraph of G.
Shinya Fujita +5 more
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Forbidden Subgraphs for Hamiltonicity of 1-Tough Graphs
Discussiones Mathematicae Graph Theory, 2016 A graph G is said to be 1-tough if for every vertex cut S of G, the number of components of G − S does not exceed |S|. Being 1-tough is an obvious necessary condition for a graph to be hamiltonian, but it is not sufficient in general.
Li Binlong +2 more
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Forbidden subgraphs on Hamiltonian index
Discrete Mathematics, 2020 Abstract Let G be a graph other than a path. The m -iterated line graph of a graph G is L m ( G ) = L ( L m − 1 ( G ) ) . where L 1 ( G ) denotes the line graph L ( G ) of G .
Xia Liu, Liming Xiong
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