Forbidden Subgraphs and Cycle Extendability

A graph G on n vertices is pancyclic if G contains cycles of all lengths`for 3 ` n and G is cycle extendable if for every nonhamiltonian cycle C G there is a cycle C 0 G such that V (C) V (C 0) and jV (C 0) n V (C)j = 1. We prove that (i) every 2-connected K 1;3-free graph is pancyclic, if G is P 5-free and n 6, if G is P 6-free and n 10, or if G is P 7-free, deer-free and n 14, and (ii) every 2-connected K 1;3-free and Z 2-free graph on n 10 vertices is cycle extend-able using at most two chords of the cycle.