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

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