Maximal K 3's and Hamiltonicity of 4-connected claw-free graphs

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Abstract

Let cl(G) denote Ryjáček's closure of a claw-free graph G. In this article, we prove the following result. Let G be a 4-connected claw-free graph. Assume that G[N G(T)] is cyclically 3-connected if T is a maximal K 3 in G which is also maximal in cl(G). Then G is hamiltonian. This result is a common generalization of Kaiser et al.'s theorem [J Graph Theory 48(4) (2005), 267-276] and Pfender's theorem [J Graph Theory 49(4) (2005), 262-272].

Original languageEnglish
Pages (from-to)40-53
Number of pages14
JournalJournal of Graph Theory
Volume70
Issue number1
DOIs
Publication statusPublished - 2012 May

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Hamiltonicity
Claw-free Graphs
Graph theory
Connected graph
Theorem
Closure
Denote
Generalization

Keywords

  • claw-free graph
  • Hamiltonian cycle
  • maximal K

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Maximal K 3's and Hamiltonicity of 4-connected claw-free graphs. / Fujisawa, Jun; Ota, Katsuhiro.

In: Journal of Graph Theory, Vol. 70, No. 1, 05.2012, p. 40-53.

Research output: Contribution to journalArticle

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