The Generalization of Dirac’s Theorem for Hypergraphs

  • Endre Szemerédi
  • Andrzej Ruciński
  • Vojtěch Rödl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Endre Szemerédi
    • 1
  • Andrzej Ruciński
    • 2
  • Vojtěch Rödl
    • 3
  1. 1.Rutgers UniversityNew Brunswick
  2. 2.A. Mickiewicz UniversityPoznańPoland
  3. 3.Emory UniversityAtlanta

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