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Notes on sufficient conditions for a graph to be Hamiltonian

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  • Michael Joseph Paul
  • Carmen Baytan Shershin
  • Anthony Connors Shershin

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.

Suggested Citation

  • Michael Joseph Paul & Carmen Baytan Shershin & Anthony Connors Shershin, 1991. "Notes on sufficient conditions for a graph to be Hamiltonian," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-3, January.
    • Handle: RePEc:hin:jijmms:875792
    DOI: 10.1155/S0161171291001138
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