The generalization of dirac's theorem for hypergraphs

  • Authors:

  • Endre Szemerédi;Andrzej Ruciński;Vojtěch Rödl

  • Affiliations:

  • Rutgers University, New Brunswick;A. Mickiewicz University, Poznań, Poland;Emory University, Atlanta, GA

  • Venue:
  • MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
  • Year:
  • 2005

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Abstract

A substantial amount of research in graph theory continues to concentrate on the existence of hamiltonian cycles and perfect matchings. A classic theorem of Dirac states that a sufficient condition for an n-vertex graph to be hamiltonian, and thus, for n even, to have a perfect matching, is that the minimum degree is at least n/2. Moreover, there are obvious counterexamples showing that this is best possible.