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Algorithmica

, Volume 68, Issue 4, pp 998–1018 | Cite as

Dominating Induced Matchings for P 7-Free Graphs in Linear Time

  • Andreas Brandstädt
  • Raffaele Mosca
Article

Abstract

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 eEE′ 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.

Keywords

Dominating induced matching Efficient edge domination P7-free graphs Linear time algorithm Robust algorithm 

Notes

Acknowledgements

The first author gratefully acknowledges a research stay at the LIMOS institute, University of Clermont-Ferrand, and the inspiring discussions with Anne Berry on dominating induced matchings.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Fachbereich InformatikUniversität RostockRostockGermany
  2. 2.Dipartimento di ScienzeUniversitá degli Studi “G. D’Annunzio”PescaraItaly

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