Finding Efficient Domination for $P_8$-Free Bipartite Graphs in Polynomial Time
| Autor: | Brandstädt, Andreas, Mosca, Raffaele |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | A vertex set $D$ in a finite undirected graph $G$ is an {\em efficient dominating set} (\emph{e.d.s.}\ for short) of $G$ if every vertex of $G$ is dominated by exactly one vertex of $D$. The \emph{Efficient Domination} (ED) problem, which asks for the existence of an e.d.s.\ in $G$, is known to be \NP-complete for $P_7$-free graphs, and even for very restricted $H$-free bipartite graph classes such as for $K_{1,4}$-free bipartite graphs as well as for $C_4$-free bipartite graphs while it is solvable in polynomial time for $P_7$-free bipartite graphs as well as for $S_{2,2,4}$-free bipartite graphs. Here we show that ED can be solved in polynomial time for $P_8$-free bipartite graphs. Comment: arXiv admin note: text overlap with arXiv:2010.16076 |
| Databáze: | arXiv |
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