A graph G is said to be pancyclic if G contains cycles of all lengths from 3 to |V (G)|. We show that if G is 4-connected, claw-free, and P10-free, then G is either pancyclic or it is the line graph of the Petersen graph. This implies that every 4-connected, claw-free, P9-free graph is pancyclic, which is best possible and extends a result of Gould et al. Pancyclicity in 3-connected graphs: Pai...

A digraph T is called a local tournament if for every vertex x of T, the set of in-neighbors as well as the set of out-neighbors of x induce tournaments. We give characterizations of generalized arc-pancyclic and strongly path-panconnected local tournaments, respectively. Our results generalize those due to Bu and Zhang (1996) about arc-pancyclic local tournaments and about strongly arc-pancycl...

Let G be a 2-connected graph of order n. For any u ∈ V (G) and l ∈ {m,m + 1, . . . , n}, if G has a cycle of length l, then G is called [m,n]pancyclic, and if G has a cycle of length l which contains u, then G is called [m,n]-vertex pancyclic. Let δ(G) be a minimum degree ofG and let NG(x) be the neighborhood of a vertex x in G. In [Australas. J. Combin. 12 (1995), 81–91] Liu, Lou and Zhao prov...