Computing role assignments of chordal graphs

  • Authors:

  • Pim van t Hof;Daniël Paulusma;Johan M. M. van Rooij

  • Affiliations:

  • School of Engineering and Computing Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, England, United Kingdom;School of Engineering and Computing Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, England, United Kingdom;Department of Information and Computing Sciences, Universiteit Utrecht, PO Box 80.089, 3508 TB Utrecht, The Netherlands

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

Quantified Score

Hi-index 5.23

Visualization

Abstract

In social network theory, a simple graph G is called k-role assignable if there is a surjective mapping that assigns a number from {1,...,k}, called a role, to each vertex of G such that any two vertices with the same role have the same sets of roles assigned to their neighbors. The decision problem whether such a mapping exists is called the k-Role Assignment problem. This problem is known to be NP-complete for any fixed k=2. In this paper, we classify the computational complexity of the k-Role Assignment problem for the class of chordal graphs. We show that for this class the problem can be solved in linear time for k=2, but remains NP-complete for any k=3. This generalizes earlier results by Sheng and answers her open problem.