Computing role assignments of chordal graphs

  • Authors:

  • Pim Van't Hof;Daniël Paulusma;Johan M. M. Van Rooij

  • Affiliations:

  • Department of Computer Science, University of Durham, Science Laboratories, Durham, England;Department of Computer Science, University of Durham, Science Laboratories, Durham, England;Department of Information and Computing Sciences, Universiteit Utrecht, Utrecht, The Netherlands

  • Venue:
  • FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

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 becomes polynomially solvable for k = 2, but remains NP-complete for any k ≥ 3. This generalizes results of Sheng and answers his open problem.