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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.


This article was originally published in Hindawi International Journal of Mathematics and Mathematical Sciences Volume 14 (1991).

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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