Release Time:2019-03-09  Hits:

Indexed by: Journal Papers

Date of Publication: 2016-01-01

Journal: ARS COMBINATORIA

Included Journals: SCIE

Volume: 124

Page Number: 95-109

ISSN: 0381-7032

Key Words: almost locally connected; claw-free graph; hamiltonian; Hamilton-connected

Abstract: G is almost locally connected if B(G) is an independent set and for any x is an element of B(G), there is a vertex y in V(G)\{x} such that N(x) boolean OR {y} induces a connected subgraph of G, where B(G) denotes the set of vertices of G that are not locally connected. In this paper, we prove that an almost locally connected claw-free graph on at least 4 vertices is Hamilton-connected if and only if it is 3-connected. This generalizes a result by Asratian that a locally connected claw-free graph on at least 4 vertices is Hamilton-connected if and only if it is 3-connected [Journal of Graph Theory 23 (1996) 191-201].