TY - JOUR
T1 - Pancyclicity of 4-connected claw-free bull-free graphs
AU - Lai, Hong Jian
AU - Zhan, Mingquan
AU - Zhang, Taoye
AU - Zhou, Ju
N1 - Publisher Copyright:
© The author(s).
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
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.
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M3 - Article
AN - SCOPUS:85082325409
SN - 1034-4942
VL - 76
SP - 366
EP - 386
JO - Australasian Journal of Combinatorics
JF - Australasian Journal of Combinatorics
IS - 3
ER -