Finding Dominating Induced Matchings in S_1,1,5-Free Graphs in Polynomial Time
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Let G=(V,E) be a finite undirected graph. An edge set E' ⊆ E is a dominating induced matching ( d.i.m.) in G if every edge in E is intersected by exactly one edge of E'. The Dominating Induced Matching (DIM) problem asks for the existence of a d.i.m. in G; this problem is also known as the Efficient Edge Domination problem; it is the Efficient Domination problem for line graphs. The DIM problem is -complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but is solvable in linear time for P_7-free graphs, and in polynomial time for S_1,2,4-free graphs as well as for S_2,2,2-free graphs and for S_2,2,3-free graphs. In this paper, combining two distinct approaches, we solve it in polynomial time for S_1,1,5-free graphs.
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