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• W1796009870 abstract "Let G be a finite undirected graph. A vertex dominates itself and its neighbors in G. A vertex set D is an efficient dominating set (e.d. for short) of G if every vertex of G is dominated by exactly one vertex of D. The Efficient Domination (ED) problem, which asks for the existence of an e.d. in G, is known to be $mathbb{NP}$ -complete even for very restricted graph classes. In particular, the ED problem remains $mathbb{NP}$ -complete for 2P 3-free graphs and thus for P 7-free graphs. We show that the weighted version of the problem (abbreviated WED) is solvable in polynomial time on various subclasses of P 7-free graphs, including (P 2 + P 4)-free graphs, P 5-free graphs and other classes. Furthermore, we show that a minimum weight e.d. consisting only of vertices of degree at most 2 (if one exists) can be found in polynomial time. This contrasts with our $mathbb{NP}$ -completeness result for the ED problem on planar bipartite graphs with maximum degree 3." @default.
• W1796009870 created "2016-06-24" @default.
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• W1796009870 date "2013-01-01" @default.
• W1796009870 modified "2023-10-01" @default.
• W1796009870 title "New Polynomial Cases of the Weighted Efficient Domination Problem" @default.
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• W1796009870 doi "https://doi.org/10.1007/978-3-642-40313-2_19" @default.
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