Computing role assignments of chordal graphs

Pim van 't Hof, Daniël Paulusma and Johan M.M. van Rooij

Theoretical Computer Science, vol. 411, no. 40-42, pp. 3601-3613, 2010.
[DOI] [Preprint]

A preliminary version of this paper appeared in the proceedings of FCT 2009, the 17th International Symposium on Fundamentals of Computation Theory (held on September 2-4, 2009 in Wrocław, Poland), Lecture Notes in Computer Science, vol. 5699, pp. 193-204.


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.