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

Oliver Cooley, Richard Mycroft

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3 Citations (Scopus)
182 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)1172-1179
Number of pages8
JournalDiscrete Mathematics
Volume340
Issue number6
Early online date20 Mar 2017
DOIs
Publication statusPublished - Jun 2017

Keywords

  • Hamilton cycle
  • Hypergraph
  • Vertex degree

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