Weighted efficient domination in two subclasses of P6-free graphs

Article Type

Research Article

Publication Title

Discrete Applied Mathematics

Abstract

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 Efficient Dominating Set (ED) problem asks for the existence of an efficient dominating set in a given graph. The ED problem is known to be solvable in polynomial time for P5-free graphs but NP-complete for P7-free graphs whereas for P6-free graphs, its complexity was an open problem. Recently, Lokshtanov et al. and independently, Mosca showed that ED is solvable in polynomial time for P6-free graphs. In this paper, we show that the ED problem can be solved efficiently for two subclasses of P6-free graphs, namely for (P6, bull)-free graphs, and for (P6,S1,1,3)-free graphs; the time bounds for the two subclasses are much better than in the general case of P6-free graphs.

First Page

38

Last Page

46

DOI

10.1016/j.dam.2015.07.032

Publication Date

3-11-2016

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