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Triangles, 4-Cycles and Parameterized (In-)Tractability

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Algorithm Theory – SWAT 2006 (SWAT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4059))

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Abstract

We show that several problems that are hard for various parameterized complexity classes on general graphs, become fixed parameter tractable on graphs with no small cycles.

More specifically, we give fixed parameter algorithms for Dominating Set, t -Vertex Cover (where we need to cover at least t edges) and several of their variants on graphs that have no triangles or cycles of length 4. These problems are known to be W[i]-hard for some i in general graphs. We also show that the Dominating Set problem is W[2]-hard in bipartite graphs and hence on triangle free graphs.

In the case of Independent Set and several of its variants, we show them fixed parameter tractable even in triangle free graphs. In contrast, we show that the Dense Subgraph problem (related to the Clique problem) is W[1]-hard on graphs with no cycles of length at most 5.

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Author information

Authors and Affiliations

  1. The Institute of Mathematical Sciences, Chennai, 600 113

    Venkatesh Raman & Saket Saurabh

Authors
  1. Venkatesh Raman
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  2. Saket Saurabh
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Editor information

Editors and Affiliations

  1. MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Lars Arge

  2. Institute of Mathematics and Computer Science, University of Latvia, Raiņa bulvāris 29, Rīga, LV-1459, Latvia

    Rusins Freivalds

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© 2006 Springer-Verlag Berlin Heidelberg

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Raman, V., Saurabh, S. (2006). Triangles, 4-Cycles and Parameterized (In-)Tractability. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_29

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  • DOI: https://doi.org/10.1007/11785293_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35753-7

  • Online ISBN: 978-3-540-35755-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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