Dominating Induced Matchings for P7-free Graphs in Linear Time

  • Andreas Brandstädt
  • Raffaele Mosca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)


Let G be a finite undirected graph with edge set E. An edge set E′ ⊆ E is an induced matching in G if the pairwise distance of the edges of E′ in G is at least two; E′ is dominating in G if every edge e ∈ E ∖ E′ intersects some edge in E′. The Dominating Induced Matching Problem (DIM, for short) asks for the existence of an induced matching E′ which is also dominating 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. However, its complexity was open for P k -free graphs for any k ≥ 5; P k denotes a chordless path with k vertices and k − 1 edges. We show in this paper that the weighted DIM problem is solvable in linear time for P 7-free graphs in a robust way.


dominating induced matching efficient edge domination P7-free graphs linear time algorithm robust algorithm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andreas Brandstädt
    • 1
  • Raffaele Mosca
    • 2
  1. 1.Institut für InformatikUniversität RostockRostockGermany
  2. 2.Dipartimento di ScienzeUniversitá degli Studi “G. D’Annunzio”PescaraItaly

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