Geodesic
Saturation number of \(tK_{l,l,l}\) in the complete tripartite graph
The electronic journal of combinatorics, Tome 28 (2021) no. 4
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For fixed graphs $F$ and $H$, a graph $G\subseteq F$ is $H$-saturated if there is no copy of $H$ in $G$, but for any edge $e\in E(F)\setminus E(G)$, there is a copy of $H$ in $G+e$. The saturation number of $H$ in $F$, denoted $sat(F,H)$, is the minimum number of edges in an $H$-saturated subgraph of $F$. In this paper, we study saturation numbers of $tK_{l,l,l}$ in complete tripartite graph $K_{n_1,n_2,n_3}$. For $t\ge 1$, $l\ge 1$ and $n_1,n_2$ and $n_3$ sufficiently large, we determine $sat(K_{n_1,n_2,n_3},tK_{l,l,l})$ exactly.
DOI : 10.37236/10116
Classification : 05C35
Mots-clés : \(tK_{l,l,l}\)-saturated graph 
@article{10_37236_10116,
     author = {Zhen He and Mei Lu},
     title = {Saturation number of {\(tK_{l,l,l}\)} in the complete tripartite graph},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {4},
     doi = {10.37236/10116},
     zbl = {1478.05080},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10116/}
}
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Zhen He; Mei Lu. Saturation number of \(tK_{l,l,l}\) in the complete tripartite graph. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/10116

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