SEARCH

SEARCH BY CITATION

Keywords:

  • hypergraphs;
  • tiling;
  • factor;
  • absorbing

Abstract

Let inline image denote the hypergraph consisting of two triples on four points. For an integer n, let inline image denote the smallest integer d so that every 3-uniform hypergraph G of order n with minimum pair-degree inline image contains inline image vertex-disjoint copies of inline image. Kühn and Osthus (J Combin Theory, Ser B 96(6) (2006), 767–821) proved that inline image holds for large integers n. Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4,

  • math image

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).