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Parameterized Graph Separation Problems

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Book cover Parameterized and Exact Computation (IWPEC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3162))

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Abstract

We consider parameterized problems where some separation property has to be achieved by deleting as few vertices as possible. The following five problems are studied: delete k vertices such that (a) each of the given ℓ terminals is separated from the others, (b) each of the given ℓ pairs of terminals are separated, (c) exactly ℓ vertices are cut away from the graph, (d) exactly ℓ connected vertices are cut away from the graph, (e) the graph is separated into ℓ components, We show that if both k and ℓ are parameters, then (a), (b) and (d) are fixed-parameter tractable, while (c) and (e) are W[1]-hard.

Research is supported in part by grants OTKA 44733, 42559 and 42706 of the Hungarian National Science Fund.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, H-1521, Hungary

    Dániel Marx

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  1. Dániel Marx
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Editor information

Editors and Affiliations

  1. School of Mathematics, Statistics, and Computer Science, Victoria University, PO Box 600, Wellington, New Zealand

    Rod Downey

  2. PCRU, Office of DVC (Research), University of Newcastle, Australia

    Michael Fellows

  3. Carleton University, Ottawa, Canada

    Frank Dehne

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© 2004 Springer-Verlag Berlin Heidelberg

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Marx, D. (2004). Parameterized Graph Separation Problems. In: Downey, R., Fellows, M., Dehne, F. (eds) Parameterized and Exact Computation. IWPEC 2004. Lecture Notes in Computer Science, vol 3162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28639-4_7

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  • DOI: https://doi.org/10.1007/978-3-540-28639-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23071-7

  • Online ISBN: 978-3-540-28639-4

  • eBook Packages: Springer Book Archive

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