Pancyclicity of 4-connected claw-free bull-free graphs

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

Pancyclicity of 4-connected claw-free bull-free graphs

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

Penn State Scranton

Research output: Contribution to journal › Article › peer-review

Abstract

AgraphG is said to be pancyclic if G contains cycles of lengths from 3to|V (G)|. The bull B(i, j) is obtained by associating one endpoint of each of the path P_i+1 and P_j+1 with distinct vertices of a triangle. In [M. Ferrara et al., Discrete Math. 313 (2013), 460–467], it was shown that every 4-connected {K_1,3,B(i, j)}-free graph with i + j = 6 is pancyclic. In this paper we show that every 4-connected {K_1,3,B(i, j)}-free graph with i + j = 7 is either pancyclic or it is the line graph of the Petersen graph.

Original language	English (US)
Pages (from-to)	366-386
Number of pages	21
Journal	Australasian Journal of Combinatorics
Volume	76
Issue number	3
State	Published - 2020

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

Cite this

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title = "Pancyclicity of 4-connected claw-free bull-free graphs",

abstract = "AgraphG is said to be pancyclic if G contains cycles of lengths from 3to|V (G)|. The bull B(i, j) is obtained by associating one endpoint of each of the path Pi+1 and Pj+1 with distinct vertices of a triangle. In [M. Ferrara et al., Discrete Math. 313 (2013), 460–467], it was shown that every 4-connected \{K1,3,B(i, j)\}-free graph with i + j = 6 is pancyclic. In this paper we show that every 4-connected \{K1,3,B(i, j)\}-free graph with i + j = 7 is either pancyclic or it is the line graph of the Petersen graph.",

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year = "2020",

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AU - Lai, Hong Jian

AU - Zhan, Mingquan

AU - Zhang, Taoye

AU - Zhou, Ju

PY - 2020

Y1 - 2020

N2 - AgraphG is said to be pancyclic if G contains cycles of lengths from 3to|V (G)|. The bull B(i, j) is obtained by associating one endpoint of each of the path Pi+1 and Pj+1 with distinct vertices of a triangle. In [M. Ferrara et al., Discrete Math. 313 (2013), 460–467], it was shown that every 4-connected {K1,3,B(i, j)}-free graph with i + j = 6 is pancyclic. In this paper we show that every 4-connected {K1,3,B(i, j)}-free graph with i + j = 7 is either pancyclic or it is the line graph of the Petersen graph.

AB - AgraphG is said to be pancyclic if G contains cycles of lengths from 3to|V (G)|. The bull B(i, j) is obtained by associating one endpoint of each of the path Pi+1 and Pj+1 with distinct vertices of a triangle. In [M. Ferrara et al., Discrete Math. 313 (2013), 460–467], it was shown that every 4-connected {K1,3,B(i, j)}-free graph with i + j = 6 is pancyclic. In this paper we show that every 4-connected {K1,3,B(i, j)}-free graph with i + j = 7 is either pancyclic or it is the line graph of the Petersen graph.

UR - https://www.scopus.com/pages/publications/85082325409

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M3 - Article

AN - SCOPUS:85082325409

SN - 1034-4942

VL - 76

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EP - 386

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

IS - 3

ER -

Pancyclicity of 4-connected claw-free bull-free graphs

Abstract

All Science Journal Classification (ASJC) codes

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