An approximate Dirac-type theorem for k-uniform hypergraphs

Authors:
Vojtĕch Rödl;Endre Szemerédi;Andrzej Ruciński
Affiliations:
Department of Mathematics and Computer Science, Emory University, Atlanta, USA 30322;Department of Computer Science, Rutgers University, Piscataway, USA 08854-8019;Department of Discrete Mathematics, A. Mickiewicz University, Poznań, Poland 61-614
Venue:
Combinatorica
Year:
2008

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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 驴 3 and 驴 0, and for all n large enough, a sufficient condition for an n-vertex k-uniform hypergraph to be hamiltonian is that each (k 驴 1)-element set of vertices is contained in at least (1/2 + 驴)n edges.