Tiling 3-uniform hypergraphs with K43-2e

Andrzej Czygrinow, Louis Debiasio, Brendan Nagle

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Let K43-2e denote the hypergraph consisting of two triples on four points. For an integer n, let t(n,K43-2e) denote the smallest integer d so that every 3-uniform hypergraph G of order n with minimum pair-degree δ2(G)≥d contains ⌊n/4⌋ vertex-disjoint copies of K43-2e. Kühn and Osthus (J Combin Theory, Ser B 96(6) (2006), 767-821) proved that t(n,K43-2e)=n4(1+o(1)) holds for large integers n. Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4, A main ingredient in our proof is the recent "absorption technique" of Rödl, Ruciński, and Szemerédi (J. Combin. Theory Ser. A 116(3) (2009), 613-636).

Original languageEnglish (US)
Pages (from-to)124-136
Number of pages13
JournalJournal of Graph Theory
Volume75
Issue number2
DOIs
StatePublished - Feb 2014

Keywords

  • absorbing
  • factor
  • hypergraphs
  • tiling

ASJC Scopus subject areas

  • Geometry and Topology

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