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arXiv · 1606.05616

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

Oliver Cooley·Richard Mycroft
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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, Böttcher, Cooley and Mycroft.

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Oliver Cooley, Richard Mycroft. 2016-06-17. The minimum vertex degree for an almost-spanning tight cycle in a $3$-uniform hypergraph. https://arxiv.org/abs/1606.05616

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