Hamilton cycles in quasirandom hypergraphs

John Lenz, Dhruv Mubayi, Richard Mycroft

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
129 Downloads (Pure)

Abstract

We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω(nk-1) contains a loose Hamilton cycle. We also give a construction to show that a k-uniform hypergraph satisfying these conditions need not contain a Hamilton ℓ-cycle if k– ℓ divides k. The remaining values of ℓ form an interesting open question. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016
Original languageEnglish
JournalRandom Structures and Algorithms
Early online date26 Feb 2016
DOIs
Publication statusE-pub ahead of print - 26 Feb 2016

Keywords

  • hypergraphs
  • Hamilton cycles
  • quasirandomness

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