Notes on sufficient conditions for a graph to be Hamiltonian

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.

Keywords

• hamilton cycle
• directed graphs
• Ghouila-Houri Theorem
• strongly connected digraphs
• Dirac's Theorem
• Ore's Theorem
• edge condition.