International Journal of Mathematics and Mathematical Sciences 
Volume 14 (1991), Issue 4, Pages 825-827
doi:10.1155/S0161171291001138

Notes on sufficient conditions for a graph to be Hamiltonian

Michael Joseph Paul,1 Carmen Baytan Shershin,2 and Anthony Connors Shershin3

 1School of Computer Science, Florida International University, Miami 33199, Florida, USA
2Mathematics Department, Ransom-Everglades School, Coconut Grove 33133, Florida, USA
3Mathematics Department, Florida International University, Miami 33199, Florida, USA
Received 1 October 1990; Revised 8 December 1990

Abstract

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.