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Wheel-Free Deletion Is W[2]-Hard

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Parameterized and Exact Computation (IWPEC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5018))

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Abstract

We show that the two problems of deciding whether k vertices or k edges can be deleted from a graph to obtain a wheel-free graph is W[2]-hard. This immediately implies that deciding whether k edges can be added to obtain a graph that contains no complement of a wheel as an induced subgraph is W[2]-hard, thereby resolving an open problem of Heggernes et al. [7] (STOC07) who ask whether there is a polynomial time recognizable hereditary graph class Π with the property that computing the minimum Π-completion is W[t]-hard for some t.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    Daniel Lokshtanov

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  1. Daniel Lokshtanov
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Martin Grohe Rolf Niedermeier

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© 2008 Springer-Verlag Berlin Heidelberg

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Lokshtanov, D. (2008). Wheel-Free Deletion Is W[2]-Hard. In: Grohe, M., Niedermeier, R. (eds) Parameterized and Exact Computation. IWPEC 2008. Lecture Notes in Computer Science, vol 5018. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79723-4_14

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  • DOI: https://doi.org/10.1007/978-3-540-79723-4_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79722-7

  • Online ISBN: 978-3-540-79723-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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