论文标题
$ k_4^ - $ - 覆盖物和$ k_5^ - $ - 覆盖的确切最小代码阈值
Exact minimum codegree thresholds for $K_4^-$-covering and $K_5^-$-covering
论文作者
论文摘要
鉴于两个$ 3 $ -Graphs $ f $和$ h $，$ f $ $ h $的$ h $是$ h $中的$ f $的副本集合，因此每个顶点$ h $至少包含在其中的至少一个副本中。令{$ c_2（n，f）$}为最大整数$ t $，以便每3块最小代码大于$ t $的3颗粒具有$ f $覆盖。在此注释中，我们通过确定{$ c_2（n，k_4^ - ）$}的确切值和{$ c_2（n，k_5^ - ）$}的确切值来回答一个空旷的问题（siam J. iNvete Math。，2016），其中$ k_t^ - $是$ 3 $ -Graph，与$ 3 $ -Graph一起使用$ 3 $ -Graph。
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.
