Cycles through particular subgraphs of claw-free graphs

@article{Broersma1995CyclesTP,
title={Cycles through particular subgraphs of claw-free graphs},
author={Haitze J. Broersma and Minggen Lu},
journal={Journal of Graph Theory},
year={1995},
volume={20},
pages={459-465}
}

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 a3(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… CONTINUE READING