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Algorithms Solving the Matching Cut Problem

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Algorithms and Complexity (CIAC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9079))

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Abstract

In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete. This paper provides a first branching algorithm solving Matching Cut in time \(O^*(2^{n/2})=O^*(1.4143^n)\) for an \(n\)-vertex input graph, and shows that Matching Cut parameterized by vertex cover number \(\tau (G)\) can be solved by a single-exponential algorithm in time \(2^{\tau (G)} O(n^2)\). Moreover, the paper also gives a polynomially solvable case for Matching Cut which covers previous known results on graphs of maximum degree three, line graphs, and claw-free graphs.

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique Théorique et Appliquée, Université de Lorraine, 57045, Metz Cedex 01, France

    Dieter Kratsch

  2. Institut für Informatik, Universität Rostock, Rostock, Germany

    Van Bang Le

Authors
  1. Dieter Kratsch
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  2. Van Bang Le
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Correspondence to Van Bang Le .

Editor information

Editors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France

    Vangelis Th. Paschos

  2. Inst. of Theoretical Computer Science, ETH Zürich, Zürich, Switzerland

    Peter Widmayer

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Kratsch, D., Le, V.B. (2015). Algorithms Solving the Matching Cut Problem. In: Paschos, V., Widmayer, P. (eds) Algorithms and Complexity. CIAC 2015. Lecture Notes in Computer Science(), vol 9079. Springer, Cham. https://doi.org/10.1007/978-3-319-18173-8_21

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  • DOI: https://doi.org/10.1007/978-3-319-18173-8_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18172-1

  • Online ISBN: 978-3-319-18173-8

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