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 1

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Keywords

  • Hamiltonian cycle
  • claw-free graph
  • maximal K

ASJC Scopus subject areas

  • Geometry and Topology

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