Strong sufficient conditions for the existence of Hamiltonian circuits in undirected graphs

AbstractIn this paper, we derive some results giving sufficient conditions for a graph G containing a Hamiltonian path to be Hamiltonian. In particular the Bondy-Chvátal theorem [J. A. Bondy and V. Chvátal, Discrete Math. 15 (1976), 111–135] is derived as a corollary of the main theorem of this paper and hence a more powerful closure operation than the one introduced by Bondy and Chvátal is defined. These results can be viewed as a step towards a unification of the various known results on the existence of Hamiltonian circuits in undirected graphs. Moreover, Theorem 1 of this paper provides a counterpart of the Chvátal-Erdös theorem [V. Chvátal and P. Erdös, Discrete Math. 2 (1972), 111–113] which gives a sufficient condition for a Hamiltonian circuit in terms of global vertex connectivity and independence number