Forbidden subgraphs for hamiltonicity of 1-tough graphs

Haitze J. Broersma, Binlong Li, Shenggui Zhang

Research output: Contribution to journal › Article › Academic › peer-review

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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
Publication statusPublished - 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. 2016 ; Vol. 36, No. 4. pp. 915-929.
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Broersma, HJ, Li, B & Zhang, S 2016, 'Forbidden subgraphs for hamiltonicity of 1-tough graphs' Discussiones mathematicae. Graph theory, vol. 36, no. 4, pp. 915-929. https://doi.org/10.7151/dmgt.1897

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: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Forbidden subgraphs for hamiltonicity of 1-tough graphs

AU - Broersma, Haitze J.

AU - Li, Binlong

AU - Zhang, Shenggui

N1 - 10.7151/dmgt.1897

PY - 2016/10

Y1 - 2016/10

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.

AB - 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.

KW - MSC-05C07

KW - Hamiltonian graph

KW - MSC-05C45

KW - MSC-05C38

KW - H-free graph

KW - Forbidden subgraph

KW - IR-101997

KW - 1-tough

KW - METIS-319456

KW - EWI-27290

KW - Toughness

U2 - 10.7151/dmgt.1897

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JO - Discussiones mathematicae. Graph theory

JF - Discussiones mathematicae. Graph theory

SN - 1234-3099

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Broersma HJ, Li B, Zhang S. Forbidden subgraphs for hamiltonicity of 1-tough graphs. Discussiones mathematicae. Graph theory. 2016 Oct;36(4):915-929. https://doi.org/10.7151/dmgt.1897

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