A Fan-type heavy triple of subgraphs for pancyclicity of 2-connected graphs

Let H denote the hourglass, a graph consisting of two triangles that have exactly one vertex in common. In this paper we prove that every 2-connected {K1,3,P7,H}-f1-heavy graph on at least nine vertices is pancyclic or missing only one cycle. This result extends the previous work by Faudree, Ryjáček and Schiermeyer.