On Traceability of Claw-o-1-heavy Graphs

A graph is called traceable if it contains a Hamilton path, i.e., a path passing through all the vertices. Let G be a graph on n vertices. G is called claw-o(-1)-heavy if every induced claw (K-1,K-3) of G has a pair of nonadjacent vertices with degree sum at least n - 1 in G. In this paper we show that a claw-o(-1)-heavy graph G is traceable if we impose certain additional conditions on G involving forbidden induced subgraphs.