Minimum codegree threshold for $C_6^3$-factors in $3$-uniform Hypergraphs

Abstract

Let $C_6^3$ be the 3-uniform hypergraph on $\{1,\dots ,6\}$ with edges $123,345,561$, which can be seen as the triangle in 3-uniform hypergraphs. For sufficiently large $n$ divisible by 6, we show that every $n$-vertex 3-uniform hypergraph $H$ with minimum codegree at least $n/3$ contains a $C_6^3$-factor, i.e., a spanning subhypergraph consisting of vertex-disjoint copies of $C_6^3$. The minimum codegree condition is best possible. This improves the asymptotical result obtained by Mycroft and answers a question of Rödl and Ruciński exactly.

21 pages, 0 figure

References in corpus (2)

• Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs
• A note on perfect matchings in uniform hypergraphs

Cited by in corpus (1)

• Codegree thresholds for covering 3-uniform hypergraphs