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International Symposium on Algorithms and Computation

ISAAC 2011: Algorithms and Computation pp 100–109Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7074))

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 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.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Rostock, D-18051, Rostock, Germany

    Andreas Brandstädt

  2. Dipartimento di Scienze, Universitá degli Studi “G. D’Annunzio”, Pescara, 65121, Italy

    Raffaele Mosca

Authors
  1. Andreas Brandstädt
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  2. Raffaele Mosca
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Editor information

Editors and Affiliations

  1. Chuo University, Kasuga, Bunkyo-ku, 112-8551, Tokyo, Japan

    Takao Asano

  2. Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

  3. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Yoshio Okamoto

  4. Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8552, Tokyo, Japan

    Osamu Watanabe

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© 2011 Springer-Verlag Berlin Heidelberg

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Brandstädt, A., Mosca, R. (2011). Dominating Induced Matchings for P 7-free Graphs in Linear Time. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_12

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  • DOI: https://doi.org/10.1007/978-3-642-25591-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25590-8

  • Online ISBN: 978-3-642-25591-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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