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arXiv · 2002.00353

Exact minimum codegree thresholds for $K_4^-$-covering and $K_5^-$-covering

Lei Yu·Xinmin Hou·Boyuan Liu·Yue Ma
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Abstract

Given two $3$-graphs $F$ and $H$, an $F$-covering of $H$ is a collection of copies of $F$ in $H$ such that each vertex of $H$ is contained in at least one copy of them. Let {$c_2(n,F)$} be the maximum integer $t$ such that every 3-graph with minimum codegree greater than $t$ has an $F$-covering. In this note, we answer an open problem of Falgas-Ravry and Zhao (SIAM J. Discrete Math., 2016) by determining the exact value of {$c_2(n, K_4^-)$} and {$c_2(n, K_5^-)$}, where $K_t^-$ is the complete $3$-graph on $t$ vertices with one edge removed.

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Lei Yu, Xinmin Hou, Boyuan Liu, Yue Ma. 2020-02-02. Exact minimum codegree thresholds for $K_4^-$-covering and $K_5^-$-covering. https://arxiv.org/abs/2002.00353

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