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König Deletion Sets and Vertex Covers above the Matching Size

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Algorithms and Computation (ISAAC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5369))

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Abstract

A graph is König-Egerváry if the size of a minimum vertex cover equals the size of a maximum matching in the graph. We show that the problem of deleting at most k vertices to make a given graph König-Egerváry is fixed-parameter tractable with respect to k. This is proved using interesting structural theorems on matchings and vertex covers which could be useful in other contexts.

We also show an interesting parameter-preserving reduction from the vertex-deletion version of red/blue-split graphs [4,9] to a version of Vertex Cover and as a by-product obtain

  1. 1

    the best-known exact algorithm for the optimization version of Odd Cycle Transversal [15];

  2. 1

    fixed-parameter algorithms for several vertex-deletion problems including the following: deleting k vertices to make a given graph (a) bipartite [17], (b) split [5], and (c) red/blue-split [7].

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Author information

Authors and Affiliations

  1. Indian Institute of Technology, Chennai, 600 036, India

    Sounaka Mishra

  2. The Institute of Mathematical Sciences, Chennai, 600 113, India

    Venkatesh Raman & Somnath Sikdar

  3. The University of Bergen, Norway

    Saket Saurabh

Authors
  1. Sounaka Mishra
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  2. Venkatesh Raman
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  3. Saket Saurabh
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  4. Somnath Sikdar
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Editor information

Editors and Affiliations

  1. School of Information Technologies, University of Sydney, Australia

    Seok-Hee Hong

  2. Graduate School of Informatics, Kyoto University, 606-8501, Kyoto, Japan

    Hiroshi Nagamochi

  3. Graduate School of Informatics, Kyoto University, Japan

    Takuro Fukunaga

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Mishra, S., Raman, V., Saurabh, S., Sikdar, S. (2008). König Deletion Sets and Vertex Covers above the Matching Size. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_73

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  • DOI: https://doi.org/10.1007/978-3-540-92182-0_73

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92181-3

  • Online ISBN: 978-3-540-92182-0

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