Forbidden subgraphs for hamiltonicity of 1-tough graphs

Haitze J. Broersma, Binlong Li, Shenggui Zhang

Abstract

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 = K_1 ∪ P_4 as the only open case.
Original languageUndefined
Pages (from-to)915-929
Number of pages15
JournalDiscussiones mathematicae. Graph theory
Volume36
Issue number4
DOIs
StatePublished - Oct 2016

Keywords

  • MSC-05C07
  • Hamiltonian graph
  • MSC-05C45
  • MSC-05C38
  • H-free graph
  • Forbidden subgraph
  • IR-101997
  • 1-tough
  • METIS-319456
  • EWI-27290
  • Toughness

Cite this

Broersma, Haitze J.; Li, Binlong; Zhang, Shenggui / Forbidden subgraphs for hamiltonicity of 1-tough graphs.

In: Discussiones mathematicae. Graph theory, Vol. 36, No. 4, 10.2016, p. 915-929.

Research output: Scientific - peer-reviewArticle

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keywords = "MSC-05C07, Hamiltonian graph, MSC-05C45, MSC-05C38, H-free graph, Forbidden subgraph, IR-101997, 1-tough, METIS-319456, EWI-27290, Toughness",
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Forbidden subgraphs for hamiltonicity of 1-tough graphs. / Broersma, Haitze J.; Li, Binlong; Zhang, Shenggui.

In: Discussiones mathematicae. Graph theory, Vol. 36, No. 4, 10.2016, p. 915-929.

Research output: Scientific - peer-reviewArticle

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AU - Zhang,Shenggui

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N2 - 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 = K_1 ∪ P_4 as the only open case.

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KW - Hamiltonian graph

KW - MSC-05C45

KW - MSC-05C38

KW - H-free graph

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KW - IR-101997

KW - 1-tough

KW - METIS-319456

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