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Indexed by:Journal Papers

Date of Publication:2016-01-01

Journal:ARS COMBINATORIA

Included Journals:SCIE

Volume:124

Page Number:95-109

ISSN No.: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].