Weighted efficient domination in two subclasses of P6-free graphs
نویسندگان
چکیده
منابع مشابه
Weighted Efficient Domination in Classes of P6-free Graphs
In a graph G, an efficient dominating set is a subset D of vertices such that D is an independent set and each vertex outside D has exactly one neighbor in D. The Minimum Weight Efficient Dominating Set (Min-WED) problem asks for an efficient dominating set of total minimum weight in a given vertex-weighted graph; the Maximum Weight Efficient Dominating Set (Max-WED) problem is defined similarl...
متن کاملWeighted Efficient Domination for $P_6$-Free Graphs in Polynomial Time
In a finite undirected graph G = (V,E), a vertex v ∈ V dominates itself and its neighbors in G. A vertex set D ⊆ V is an efficient dominating set (e.d. for short) of G if every v ∈ V is dominated in G 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 NP-complete for P7-free graphs but solvable in linear time for P5-fr...
متن کاملWeighted Efficient Domination for P5-Free Graphs in Linear Time
In a finite undirected graph G = (V,E), a vertex v ∈ V dominates itself and its neighbors. A vertex set D ⊆ V in G 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 NP-complete for P7-free graphs but solvable in polynomial time for ...
متن کاملWeighted independent sets in a subclass of P6-free graphs
TheMaximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. The complexity of the MWIS problem for P6-free graphs is unknown. In this note, we show that the MWIS problem can be solved in time O(nm) for (P6, banner)-free graphs by analyzing the structure of subclasses of these class of graphs. This extend...
متن کاملEfficient Domination for Some Subclasses of P_6 -free Graphs in Polynomial Time
Let G be a finite undirected graph. A vertex dominates itself and all 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 NP-complete even for very restricted graph classes such as P7-free chordal gr...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.07.032