Physical Sciences and Mathematics Commons^™

Notes On Sufficient Conditions For A Graph To Be Hamiltonian, Michael Joseph Paul, Carmen Baytan Shershin, Anthony Connors Shershin

School of Computing and Information Sciences

The first part of this paper deals with an extension of Dirac's Theorem to directed graphs. It is related to a result often referred to as the Ghouila-Houri Theorem. Here we show that the requirement of being strongly connected in the hypothesis of the Ghouila-Houri Theorem is redundant.

The Second part of the paper shows that a condition on the number of edges for a graph to be hamiltonian implies Ore's condition on the degrees of the vertices.