A Sufficient Condition on Degree Sums of Independent Triples for Hamiltonian Cycles in 1-Tough Graphs

Abstract

We prove that if $G$ is a 1-tough graph with $n=|V(G)|\ge 13$ such that
the degree sum of any three independent vertices is at least $\frac{3n-14}{2}$, then $G$ is hamiltonian.