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 Paul1
, Carmen Baytan Shershin2
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
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.