Exact minimum codegree threshold for K-4-factors
Research output: Contribution to journal › Article › peer-review
Colleges, School and Institutes
Given hypergraphs F and H, an F-factor in H is a set of vertex-disjoint copies of F which cover all the vertices in H. Let K − 4 denote the 3-uniform hypergraph with four vertices and three edges. We show that for sufficiently large n ∈ 4ℕ, every 3-uniform hypergraph H on n vertices with minimum codegree at least n/2−1 contains a K − 4-factor. Our bound on the minimum codegree here is best possible. It resolves a conjecture of Lo and Markström  for large hypergraphs, who earlier proved an asymptotically exact version of this result. Our proof makes use of the absorbing method as well as a result of Keevash and Mycroft  concerning almost perfect matchings in hypergraphs.
|Journal||Combinatorics, Probability and Computing|
|Publication status||Published - 4 Aug 2017|
- math.CO, 05C35, 05C65, 05C70, primary 05C70, secondary 05C35, 05C65