Combinatorica

, Volume 28, Issue 2, pp 229–260

# An approximate Dirac-type theorem for k-uniform hypergraphs

• Vojtěch Rödl
• 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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## 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