Minimum codegree threshold for (K43e)-factors

https://doi.org/10.1016/j.jcta.2012.12.005Get rights and content
Under an Elsevier user license
open archive

Abstract

Given hypergraphs H and F, an F-factor in H is a spanning subgraph consisting of vertex-disjoint copies of F. Let K43e denote the 3-uniform hypergraph on 4 vertices with 3 edges. We show that for any γ>0 there exists an integer n0 such that every 3-uniform hypergraph H of order n>n0 with minimum codegree at least (1/2+γ)n and 4|n contains a (K43e)-factor. Moreover, this bound is asymptotically the best possible and we further give a conjecture on the exact value of the threshold for the existence of a (K43e)-factor. Thereby, all minimum codegree thresholds for the existence of F-factors are known asymptotically for 3-uniform hypergraphs F on 4 vertices.

Keywords

Hypergraph
3-Graph
Factorization
Minimum codegree

Cited by (0)

1

The first author was supported by the ERC, grant no. 258345.