  A graph is called traceable if it contains a Hamilton path, i.e., a path
passing through all its 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.
