Forbidden subgraphs for hamiltonicity of 1-tough graphs

Binlong Li; Hajo J. Broersma; Shenggui Zhang

doi:10.7151/dmgt.1897

Forbidden subgraphs for hamiltonicity of 1-tough graphs

Binlong Li
, Hajo J. Broersma
, Shenggui Zhang

School of Mathematics and Statistics

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

9 Scopus citations

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 = K₁ ∪ P₄ as the only open case.

Original language	English
Pages (from-to)	915-929
Number of pages	15
Journal	Discussiones Mathematicae - Graph Theory
Volume	36
Issue number	4
DOIs	https://doi.org/10.7151/dmgt.1897
State	Published - 2016

Keywords

1-tough graph
Forbidden subgraph
H-free graph
Hamiltonian graph

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10.7151/dmgt.1897

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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 = K1 ∪ P4 as the only open case.",

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AU - Broersma, Hajo J.

AU - Zhang, Shenggui

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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 = K1 ∪ P4 as the only open case.

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KW - Forbidden subgraph

KW - H-free graph

KW - Hamiltonian graph

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IS - 4

ER -

Forbidden subgraphs for hamiltonicity of 1-tough graphs

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Keywords

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