Generalized Above Guarantee Vertex Cover and r-Partization

  • R. Krithika
  • N. S. Narayanaswamy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7157)

Abstract

Vertex cover and odd cycle transversal are minimum cardinality sets of vertices of a graph whose deletion makes the resultant graph 1-colorable and 2-colorable, respectively. As a natural generalization of these well-studied problems, we consider the Graph r-Partization problem of finding a minimum cardinality set of vertices whose deletion makes the graph r-colorable. We explore further connections to Vertex Cover by introducing Generalized Above Guarantee Vertex Cover, a variant of Vertex Cover defined as: Given a graph G, a clique cover \(\cal K\) of G and a non-negative integer k, does G have a vertex cover of size at most \(k+\sum_{C \in \cal K}(|C|-1)\)? We study the parameterized complexity hardness of this problem by a reduction from r-Partization. We then describe sequacious fixed-parameter tractability results for r-Partization, parameterized by the solution size k and the required chromaticity r, in perfect graphs and split graphs. For Odd Cycle Transversal, we describe an O*(2k) algorithm for perfect graphs and a polynomial-time algorithm for co-chordal graphs.

Keywords

Parameterized complexity Generalized above guarantee vertex cover Odd cycle transversal r-Partization Perfect graphs Split graphs 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • R. Krithika
    • 1
  • N. S. Narayanaswamy
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology MadrasIndia

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