Forbidden subgraphs for chorded pancyclicity

We call a graph Gpancyclic if it contains at least one cycle of every possible length m, for 3≤m≤|V(G)|. In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs sufficient to imply that the graph contains at least one chorded cycle of every possible length 4,5,…,|V(G)|. In particular, certain paths and triangles with pendant paths are forbidden.