Pancyclicity of 4-Connected, Claw-Free, P10-Free Graphs
نویسندگان
چکیده
A graph G is said to be pancyclic if G contains cycles of all lengths from 3 to |V (G)|. We show that if G is 4-connected, claw-free, and P10-free, then G is either pancyclic or it is the line graph of the Petersen graph. This implies that every 4-connected, claw-free, P9-free graph is pancyclic, which is best possible and extends a result of Gould et al. Pancyclicity in 3-connected graphs: Pairs of forbidden subgraphs, [J Graph Theory 47 (2004), 183–202]. C © 2012 Wiley Periodicals, Inc. J. Graph Theory 00: 1–13, 2012
منابع مشابه
Pancyclicity of 3-connected graphs: Pairs of forbidden subgraphs
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ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 71 شماره
صفحات -
تاریخ انتشار 2012