, Volume 77, Issue 4, pp 1283–1302 | Cite as

Finding Dominating Induced Matchings in \(P_8\)-Free Graphs in Polynomial Time

  • Andreas BrandstädtEmail author
  • Raffaele Mosca


Let \(G=(V,E)\) be a finite undirected graph. An edge set \(E' \subseteq E\) 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. The DIM problem is related to parallel resource allocation problems, encoding theory and network routing. It is \({\mathbb {NP}}\)-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree three and is solvable in linear time for \(P_7\)-free graphs. However, its complexity was open for \(P_k\)-free graphs for any \(k \ge 8\); \(P_k\) denotes the chordless path with k vertices and \(k-1\) edges. We show in this paper that the weighted DIM problem is solvable in polynomial time for \(P_8\)-free graphs.


Dominating induced matching Efficient edge domination  \(P_8\)-free graphs Polynomial time algorithm 



The authors gratefully thank three anonymous reviewers for their helpful comments. The second author would like to witness that he just tries to pray a lot and is not able to do anything without that.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institut für InformatikUniversität RostockRostockGermany
  2. 2.Dipartimento di EconomiaUniversitá degli Studi “G. D’Annunzio”PescaraItaly

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