Hamiltonian Connectedness in Claw-Free Graphs

Abstract.

 In this paper, we show the following two results.

(1). Let G be a 3-connected claw-free graph and H a subgraph of G with . Then G is H-connected (i.e., for any two vertices u and v in G, G has a path connecting u and v and containing all vertices of H). This result generalizes the result of Wu, Cha and Jin that G is Hamiltonian connected if the degree sum of any pairwise nonadjacent vertices is at least .

(2). Every k-connected claw-free graph on at most vertices is Hamiltonian connected. This result further extends the result of Z. Wu, Q. Cha and Y. Jin.