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Pathwidth and Searching in Parameterized Threshold Graphs

  • D. Sai Krishna
  • T. V. Thirumala Reddy
  • B. Sai Shashank
  • C. Pandu Rangan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)

Abstract

Treewidth and pathwidth are important graph parameters that represent how close the graph is to trees and paths respectively. We calculate treewidth and pathwidth on parameterized chordal and threshold graphs. We define a chordal + 1v graph as a graph that can be made into a chordal graph by removing a vertex. We give polynomial time algorithms for computing the treewidth of a chordal + 1v graph, pathwidth of a threshold + 1v graph and a threshold + 2e graph. The mixed search number of a graph is the minimum number of cops required to capture a single robber, who is hiding in the graph. We apply the algorithm to compute the pathwidth in order to compute the mixed search number of a threshold + 1v graph.

Keywords

Graph searching treewidth pathwidth parameterization threshold graphs 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • D. Sai Krishna
    • 1
  • T. V. Thirumala Reddy
    • 1
  • B. Sai Shashank
    • 2
  • C. Pandu Rangan
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology MadrasChennaiIndia
  2. 2.Department of Computer Science and EngineeringIndian Institute of Technology GuwahatiGuwahatiIndia

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