Finding Efficient Domination for $S_{1,1,5}$-Free Bipartite Graphs in Polynomial Time
| Autor: | Brandstädt, Andreas, Mosca, Raffaele |
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| Rok vydání: | 2020 |
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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} (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 \NP-complete for various $H$-free bipartite graphs, e.g., Lu and Tang showed that ED is \NP-complete for chordal bipartite graphs and for planar bipartite graphs; actually, ED is \NP-complete even for planar bipartite graphs with vertex degree at most 3 and girth at least $g$ for every fixed $g$. Thus, ED is \NP-complete for $K_{1,4}$-free bipartite graphs and for $C_4$-free bipartite graphs. In this paper, we show that ED can be solved in polynomial time for $S_{1,1,5}$-free bipartite graphs. Comment: arXiv admin note: text overlap with arXiv:2008.04046 |
| Databáze: | arXiv |
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