A Quartic Kernel for Pathwidth-One Vertex Deletion

  • Geevarghese Philip
  • Venkatesh Raman
  • Yngve Villanger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)


The pathwidth of a graph is a measure of how path-like the graph is. Given a graph G and an integer k, the problem of finding whether there exist at most k vertices in G whose deletion results in a graph of pathwidth at most one is NP-Complete. We initiate the study of the parameterized complexity of this problem, parameterized by k. We show that the problem has a quartic vertex-kernel: We show that, given an input instance (G = (V,E),k);|V| = n, we can construct, in polynomial time, an instance (G′,k′) such that (i) (G,k) is a YES instance if and only if (G′,k′) is a YES instance, (ii) G′ has \({\mathcal O}(k^{4})\) vertices, and (iii) k′ ≤ k. We also give a fixed parameter tractable (FPT) algorithm for the problem that runs in \({\mathcal O}(7^{k}k\cdot n^{2})\) time.


Parameterized Complexity Polynomial Kernel Tree Decomposition Layout Problem Reduction Rule 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Geevarghese Philip
    • 1
  • Venkatesh Raman
    • 1
  • Yngve Villanger
    • 2
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.University of BergenBergenNorway

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