Pathwidth and searching in parameterized threshold graphs

  • Authors:

  • D. Sai Krishna;T. V. Thirumala Reddy;B. Sai Shashank;C. Pandu Rangan

  • Affiliations:

  • Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India;Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India;Department of Computer Science and Engineering, Indian Institute of Technology Guwahati, Guwahati, India;Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India

  • Venue:
  • WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
  • Year:
  • 2010

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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.