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International Journal of Mathematics and Mathematical Sciences
Volume 14, Issue 4, Pages 825-827

Notes on sufficient conditions for a graph to be Hamiltonian

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

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.