Forbidden Subgraphs Generating Almost All Claw-Free Graphs with High Connectivity

抄録

For a family H of connected graphs and an integer k≥1, let G_k(H) denote the family of k-connected graphs which contain no element of H as an induced subgraph. Let H⁺ be the family of those connected graphs of order 5 which contain K_1,3 as an induced subgraph. In this paper, for each integer k≥1, we characterize the families H⊆H⁺ such that the symmetric difference of G_k(K_1,3) and G_k(H) is finite.