Best monotone degree conditions for binding number and cycle structure

Woodall has shown that every 3/2-binding graph is hamiltonian. In this paper, we consider best monotone degree conditions for a bb-binding graph to be hamiltonian, for 1≤b<3/21≤b<3/2. We first establish such a condition for b=1b=1. We then give a best monotone degree condition for a bb-binding graph to be 1-tough, for 1