Unifying Results On Hamiltonian Claw-Free Graphs

Abstract

This work was motivated by many (recent) papers on hamiltonicity of claw-free graphs, i.e. graphs that do not contain K 1;3 as an induced subgraph. By combining ideas from these papers with some new observations, we unify several of the existing sufficiency results, using a new sufficient condition consisting of seven subconditions. If each pair of vertices at distance two of a 2-connected claw-free graph G satisfies at least one of these subconditions, then G is hamiltonian. We also present infinite classes of examples of graphs showing that these subconditions are, in some sense, independent. AMS Subject Classifications (1991): 05 C 45 Key words: claw-free graph, hamiltonian graph, degree condition, local connectivity, forbidden subgraph Part of the work was done while subsets of the authors met at Aachen and Plzen. The work of the second and third author was supported by EC-grant No. 927. 1 1. TERMINOLOGY AND NOTATION We use [1] for terminology and notation not defined here and co..