Cycles through particular subgraphs of claw‐free graphs
Hajo J. Broersma, Mei Lu · Journal of Graph Theory · 1995
Abstract Let G be a 2‐connected claw‐free graph on n vertices, and let H be a subgraph of G. We prove that G has a cycle containing all vertices of H whenever α3(H) ≧ κ(G), where α3(H) denotes the maximum number of vertices of H that are pairwise at distance at least three in G, and κ(G) denotes the connectivity of G. This result is an analog of a result from the thesis of Fournier, and generalizes the result of Zhang that G is hamiltonian if the degree sum of any κ(G) + 1 pairwise nonadjacent vertices is at least n − κ(G). © 1995 John Wiley & Sons, Inc.