Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs

Christian Reiher; Vojtěch Rödl; Andrzej Ruciński; Mathias Schacht; Endre Szemerédi

doi:10.1112/plms.12235

Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs

Combinatorics 2019-06-13 v2

Authors: Christian Reiher , Vojtěch Rödl , Andrzej Ruciński , Mathias Schacht , Endre Szemerédi

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Abstract

We show that every 3-uniform hypergraph with $n$ vertices and minimum vertex degree at least $(5/9+o(1))\binom{n}2$ contains a tight Hamiltonian cycle. Known lower bound constructions show that this degree condition is asymptotically optimal.

Keywords

3-uniform hypergraphs tight Hamiltonian cycles minimum vertex degree extremal combinatorics asymptotic optimality

Cite

@article{arxiv.1611.03118,
  title  = {Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs},
  author = {Christian Reiher and Vojtěch Rödl and Andrzej Ruciński and Mathias Schacht and Endre Szemerédi},
  journal= {arXiv preprint arXiv:1611.03118},
  year   = {2019}
}

Comments

38 pages, second version addresses changes arising from the referee reports

Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs

Abstract

Keywords

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