Critical graphs for subpancyclicity of 3-connected claw-free graphs

Let Fk be the family of graphs G such that all sufficiently large k-connected claw-free graphs which contain no induced copies of G are subpancyclic. We show that for every k≥3 the family F1k is infinite and make the first step toward the complete characterization of the family F3. 2009 Wiley Periodicals, Inc. J Graph Theory 62: 263–278, 2009 Contract grant sponsor: KBN (T. L.); Contract grant number: 2 P03A 016 23. Journal of Graph Theory 2009 Wiley Periodicals, Inc.