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

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

doi:10.1007/s00373-018-1987-4

Pancyclicity of 4-Connected { K_{1 , 3}, Z₈} -Free Graphs

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

Penn State Scranton

Research output: Contribution to journal › Article › peer-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 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 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 language	English (US)
Pages (from-to)	67-89
Number of pages	23
Journal	Graphs and Combinatorics
Volume	35
Issue number	1
DOIs	https://doi.org/10.1007/s00373-018-1987-4
State	Published - Jan 2 2019

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-018-1987-4

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title = "Pancyclicity of 4-Connected \{ K1 , 3, Z8\} -Free Graphs",

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.",

author = "Lai, \{Hong Jian\} and Mingquan Zhan and Taoye Zhang and Ju Zhou",

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AU - Lai, Hong Jian

AU - Zhan, Mingquan

AU - Zhang, Taoye

AU - Zhou, Ju

PY - 2019/1/2

Y1 - 2019/1/2

N2 - 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.

AB - 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.

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JF - Graphs and Combinatorics

IS - 1

ER -

Pancyclicity of 4-Connected { K_{1 , 3}, Z₈} -Free Graphs

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