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Graphs and Combinatorics

, Volume 35, Issue 1, pp 67–89 | Cite as

Pancyclicity of 4-Connected \(\{K_{1,3},Z_8\}\)-Free Graphs

  • Hong-Jian Lai
  • Mingquan Zhan
  • Taoye Zhang
  • Ju Zhou
Original Paper
  • 41 Downloads

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 \(Z_i\) to denote the graph obtained by identifying an endpoint of the path \(P_{i+1}\) with a vertex of a triangle. In this paper, we show that every 4-connected claw-free \(Z_8\)-free graph is either pancyclic or is the line graph of the Petersen graph. This implies that every 4-connected claw-free \(Z_6\)-free graph is pancyclic, and every 5-connected claw-free \(Z_8\)-free graph is pancyclic.

Keywords

Claw-free Pancyclic Forbidden subgraphs 

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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  • Hong-Jian Lai
    • 1
    • 2
  • Mingquan Zhan
    • 3
  • Taoye Zhang
    • 4
  • Ju Zhou
    • 5
  1. 1.Department of MathematicsWest Virginia UniversityMorgantownUSA
  2. 2.College of Mathematics and System SciencesXinjiang UniversityÜrümqiPeople’s Republic of China
  3. 3.Department of MathematicsMillersville University of PennsylvaniaMillersvilleUSA
  4. 4.Department of MathematicsPenn State Worthington ScrantonDunmoreUSA
  5. 5.Department of MathematicsKutztown University of PennsylvaniaKutztownUSA

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