# The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph

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## External organisations

• Graz Tech Univ

## Abstract

We prove that any $3$-uniform hypergraph whose minimum vertex degree is at least $\left(\frac{5}{9} + o(1) \right)\binom{n}{2}$ admits an almost-spanning tight cycle, that is, a tight cycle leaving $o(n)$ vertices uncovered. The bound on the vertex degree is asymptotically best possible. Our proof uses the hypergraph regularity method, and in particular a recent version of the hypergraph regularity lemma proved by Allen, B\"ottcher, Cooley and Mycroft.

## Details

Original language English 1172-1179 8 Discrete Mathematics 340 6 20 Mar 2017 Published - Jun 2017

## Keywords

• Hamilton cycle, Hypergraph, Vertex degree