Displaying similar documents to “Hamilton cycles in almost distance-hereditary graphs”

Forbidden Subgraphs for Hamiltonicity of 1-Tough Graphs

Binlong Li, Hajo J. Broersma, Shenggui Zhang (2016)

Discussiones Mathematicae Graph Theory

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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. We study the problem of characterizing all graphs H such that every 1-tough H-free graph is hamiltonian. We almost obtain a complete solution to this problem, leaving H = K1 ∪ P4 as the only open case.

Heavy Subgraphs, Stability and Hamiltonicity

Binlong Li, Bo Ning (2017)

Discussiones Mathematicae Graph Theory

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Let G be a graph. Adopting the terminology of Broersma et al. and Čada, respectively, we say that G is 2-heavy if every induced claw (K1,3) of G contains two end-vertices each one has degree at least |V (G)|/2; and G is o-heavy if every induced claw of G contains two end-vertices with degree sum at least |V (G)| in G. In this paper, we introduce a new concept, and say that G is S-c-heavy if for a given graph S and every induced subgraph G′ of G isomorphic to S and every maximal clique...

A classification for maximal nonhamiltonian Burkard-Hammer graphs

Ngo Dac Tan, Chawalit Iamjaroen (2008)

Discussiones Mathematicae Graph Theory

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A graph G = (V,E) is called a split graph if there exists a partition V = I∪K such that the subgraphs G[I] and G[K] of G induced by I and K are empty and complete graphs, respectively. In 1980, Burkard and Hammer gave a necessary condition for a split graph G with |I| < |K| to be hamiltonian. We will call a split graph G with |I| < |K| satisfying this condition a Burkard-Hammer graph. Further, a split graph G is called a maximal nonhamiltonian split graph if G is nonhamiltonian...

Hamiltonicity of k -traceable graphs.

Bullock, Frank, Dankelmann, Peter, Frick, Marietjie, Henning, Michael A., Oellermann, Ortrud R., van Aardt, Susan (2011)

The Electronic Journal of Combinatorics [electronic only]

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