Pancyclicity of claw-free hamiltonian graphs

A graph G on n vertices is called subpancyclic if it contains cycles of every length k with 3 less than or equal to k less than or equal to c(G), where c(G) denotes the length of a longest cycle in G; if moreover c(G) = n, then G is called pancyclic. By a result of Flandrin et al. a claw-free graph (on at least 35 vertices) with minimum degree at least 1/3(n-2) is pancyclic. This degree bound is best possible. We prove that for a claw-free graph to be subpancyclic we only need the degree condition delta > root 3n + 1 - 2. Again, this degree bound is best possible. It follows directly that under the same condition a hamiltonian claw-free graph is pancyclic. (C) 1999 Elsevier Science B.V. All rights reserved.