Pancyclicity of 4‐Connected, Claw‐Free, P10‐Free Graphs
Michael J. Ferrara, Timothy Morris, Paul S. Wenger · Journal of Graph Theory · 2012
Abstract A graph G is said to be pancyclic if G contains cycles of all lengths from 3 to . 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].