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.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics