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 _1,3 ) 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.