A Dirac-Type Theorem for 3-Uniform Hypergraphs

  • Authors:

  • Vojtěch Rödl;Andrzej Ruciński;Endre Szemerédi

  • Affiliations:

  • Emory University, Atlanta, GA, USA (e-mail: rodl@mathcs.emory.edu);A. Mickiewicz University, Poznań, Poland (e-mail: rucinski@amu.edu.pl);Rutgers University, New Brunswick, USA (e-mail: szemered@cs.rutgers.edu)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2006

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Abstract

A Hamiltonian cycle in a 3-uniform hypergraph is a cyclic ordering of the vertices in which every three consecutive vertices form an edge. In this paper we prove an approximate and asymptotic version of an analogue of Dirac's celebrated theorem for graphs: for each γ0 there exists n0 such that every 3-uniform hypergraph on $n\geq n_0$ vertices, in which each pair of vertices belongs to at least $(1/2+\gamma)n$ edges, contains a Hamiltonian cycle.