Computing Role Assignments of Chordal Graphs

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.

• Type: Conference
• Year: 2009
• Where: FCT
• Authors: Pim van 't Hof, Daniël Paulusma, Johan M. M. van Rooij
• Keywords: Decision Problem, FCT 2009, K-role Assignment Problem, Social Network Theory, Theoretical Computer Science