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Combinatorica

, Volume 28, Issue 2, pp 229–260 | Cite as

An approximate Dirac-type theorem for k-uniform hypergraphs

  • Vojtěch RödlEmail author
  • Endre Szemerédi
  • Andrzej Ruciński
Article

Abstract

A k-uniform hypergraph is hamiltonian if for some cyclic ordering of its vertex set, every k consecutive vertices form an edge. In 1952 Dirac proved that if the minimum degree in an n-vertex graph is at least n/2 then the graph is hamiltonian.

We prove an approximate version of an analogous result for uniform hypergraphs: For every K ≥ 3 and γ > 0, and for all n large enough, a sufficient condition for an n-vertex k-uniform hypergraph to be hamiltonian is that each (k − 1)-element set of vertices is contained in at least (1/2 + γ)n edges.

Mathematics Subject Classification (2000)

05C65 05C45 05D05 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Vojtěch Rödl
    • 1
    Email author
  • Endre Szemerédi
    • 2
  • Andrzej Ruciński
    • 3
  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  2. 2.Department of Computer ScienceRutgers UniversityPiscatawayUSA
  3. 3.Department of Discrete MathematicsA. Mickiewicz UniversityPoznańPoland

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