Minimum codegree threshold for $(K_4^3-e)$-factors

Details Minimum codegree threshold for $(K_4^3-e)$-factors Minimum codegree threshold for $(K_4^3-e)$-factors

2011-11-24

arxiv.org/abs/1111.5734v1

Mathematics

Combinatorics

Scientific paper

iven hypergraphs $H$ and $F$, an $F$-factor in $H$ is a spanning subgraph consisting of vertex disjoint copies of $F$. Let $K_4^3-e$ denote the 3-uniform hypergraph on 4 vertices with 3 edges. We show that for $\gamma>0$ there exists an integer $n_0$ such that every 3-uniform hypergraph $H$ of order $n > n_0$ with minimum codegree at least $(1/2+\gamma)n$ and $4|n$ contains a $(K_4^3-e)$-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 $(K_4^3-e)$-factor. Therefore, all minimum codegree thresholds for the existence of $F$-factors are known asymptotically for 3-uniform hypergraphs $F$ on 4 vertices.

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