Pancyclicity of 4-Connected { K1 , 3, Z8} -Free Graphs

Hong Jian Lai, Mingquan Zhan, Taoye Zhang, Ju Zhou

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A graph G is said to be pancyclic if G contains cycles of lengths from 3 to |V(G)|. For a positive integer i, we use Zi to denote the graph obtained by identifying an endpoint of the path Pi + 1 with a vertex of a triangle. In this paper, we show that every 4-connected claw-free Z8-free graph is either pancyclic or is the line graph of the Petersen graph. This implies that every 4-connected claw-free Z6-free graph is pancyclic, and every 5-connected claw-free Z8-free graph is pancyclic.

Original languageEnglish (US)
Pages (from-to)67-89
Number of pages23
JournalGraphs and Combinatorics
Volume35
Issue number1
DOIs
StatePublished - Jan 2 2019

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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