Results 11 to 20 of about 312 (179)
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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Forbidden Subgraphs of Power Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 The undirected power graph (or simply power graph) of a group $G$, denoted by $P(G)$, is a graph whose vertices are the elements of the group $G$, in which two vertices $u$ and $v$ are connected by an edge between if and only if either $u=v^i$ or $v=u^j$ for some $i$, $j$.
Manna, Pallabi +2 more
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Toughness, Forbidden Subgraphs and Pancyclicity [PDF]
Graphs and Combinatorics, 2021 AbstractMotivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of $$K_1\cup P_4$$
Wei Zheng, Hajo Broersma, Ligong Wang
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Splits with forbidden subgraphs [PDF]
Discrete Mathematics, 2022 In this note, we fix a graph $H$ and ask into how many vertices can each vertex of a clique of size $n$ can be "split" such that the resulting graph is $H$-free. Formally: A graph is an $(n,k)$-graph if its vertex sets is a pairwise disjoint union of $n$ parts of size at most $k$ each such that there is an edge between any two distinct parts. Let $$ f(
Maria Axenovich, Ryan R. Martin
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Forbidden subgraph decomposition
Discrete Mathematics, 2002 no ...
Rusu, Irena, Spinrad, Jeremy P.
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3-Rainbow Index and Forbidden Subgraphs [PDF]
Graphs and Combinatorics, 2017 11 ...
Li, Wenjing +2 more
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Forbidden subgraphs that imply hamiltonian‐connectedness* [PDF]
Journal of Graph Theory, 2002 AbstractIt is proven that if G is a 3‐connected claw‐free graph which is also H1‐free (where H1 consists of two disjoint triangles connected by an edge), then G is hamiltonian‐connected. Also, examples will be described that determine a finite family of graphs ${\cal L}$ such that if a 3‐connected graph being claw‐free and L‐free implies G is ...
Broersma, Haitze J. +4 more
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On hamiltonicity of 1-tough triangle-free graphs
Electronic Journal of Graph Theory and Applications, 2021 Let ω(G) denote the number of components of a graph G. A connected graph G is said to be 1-tough if ω(G − X)≤|X| for all X ⊆ V(G) with ω(G − X)>1. It is well-known that every hamiltonian graph is 1-tough, but that the reverse statement is not true in ...
Wei Zheng, Hajo Broersma, Ligong Wang
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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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Colouring graphs with forbidden bipartite subgraphs
Combinatorics, Probability and Computing, 2022 AbstractA conjecture of Alon, Krivelevich and Sudakov states that, for any graph $F$ , there is a constant $c_F \gt 0$ such that if $G$ is an $F$ -free graph of maximum degree $\Delta$ , then $\chi\!(G) \leqslant c_F \Delta/ \log\!\Delta$ . Alon, Krivelevich and Sudakov verified this conjecture for a class of graphs $F$ that includes all ...
James Anderson +2 more
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