2017/06/14 by Andreas Brandstädt, Brandstädt, Andreas, Raffaele Mosca +1
Computer Science · Social Sciences · #Advanced Graph Theory Research #Asian Industrial and Economic Development #Complexity and Algorithms in Graphs #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.1706.04894
openalex publication_date 2017/06/14 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28
Let G=(V,E) be a finite undirected graph. An edge set E' ⊆ E is a \em dominating induced matching (\em 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 \NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 and is solvable in linear time for P7-free graphs, and in polynomial time for S1,2,4-free graphs as well as for S2,2,2-free graphs. In this paper, combining two distinct approaches, we solve it in polynomial time for S2,2,3-free graphs.