Pancyclicity of 4-connected {Claw, Generalized Bull}-free Graphs

A graph G is pancyclic if it contains cycles of each length ℓ, 3 ≤ ℓ ≤ |V (G)|. The generalized bull B(i, j) is obtained by associating one endpoint of each of the paths P i+1 and P j+1 with distinct vertices of a triangle. Gould, Luczak and Pfende

Claw-free 3-connected P11-free graphs are hamiltonian

We show that every 3-connected claw-free graph which contains no induced copy of P_11 is hamiltonian. Since there exist non-hamiltonian 3-connected claw-free graphs without induced copies of P_-12 this result is, in a way, best possible