Minimum vertex degree threshold for loose Hamilton cycles in 3-uniform hypergraphs

Jie Han, Yi Zhao

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)

Abstract

We show that for sufficiently large n, every 3-uniform hypergraph on n vertices with minimum vertex degree at least (n-12)-(34n-2)+c, where c=. 2 if n∈4N and c=. 1 if n∈2N-4N, contains a loose Hamilton cycle. This degree condition is best possible and improves on the work of Buß, Hàn and Schacht who proved the corresponding asymptotical result.

Original languageEnglish
Pages (from-to)70-96
Number of pages27
JournalJournal of Combinatorial Theory. Series B
Volume114
DOIs
Publication statusPublished - 1 Sept 2015
Externally publishedYes

Keywords

  • Absorbing method
  • Hamilton cycle
  • Hypergraph
  • Regularity lemma

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