Cycles through particular subgraphs of claw-free graphs

H. J. Broersma, M. Lu
1995 Journal of Graph Theory  
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 a 3 ( H ) 5 K(G), where a 3 ( H ) denotes the maximum number of vertices of H that are pairwise at distance at least three in G, and K(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 K(G) + 1 pairwise nonadjacent vertices is at least n -K(G). 0 1995 John
doi:10.1002/jgt.3190200409 fatcat:ap5hk4ghpnf2nlmkdvhwtwgxke