Geodesic
Exact minimum codegree thresholds for \(K_4^-\)-covering and \(K_5^-\)-covering
Lei Yu ; Xinmin Hou1 ; Yue Ma ; Boyuan Liu
1University of Science and Technology of China
The electronic journal of combinatorics, Tome 27 (2020) no. 3
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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 minimum 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.
DOI : 10.37236/8784
Classification : 05C70, 05C35, 05C65
Mots-clés : 3-graphs, covering, codegree, extremal graphs

Lei Yu    ; Xinmin Hou  1   ; Yue Ma    ; Boyuan Liu 

1 University of Science and Technology of China 
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     author = {Lei Yu and Xinmin Hou and Yue Ma and Boyuan Liu},
     title = {Exact minimum codegree thresholds for {\(K_4^-\)-covering} and {\(K_5^-\)-covering}},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {3},
     doi = {10.37236/8784},
     zbl = {1445.05086},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8784/}
}
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Lei Yu; Xinmin Hou; Yue Ma; Boyuan Liu. Exact minimum codegree thresholds for \(K_4^-\)-covering and \(K_5^-\)-covering. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/8784

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