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Computing role assignments of chordal graphs. \ud

By P van 't Hof, Daniel Paulusma and J.M.M. van Rooij

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.\ud \u

Topics: Role assignment, Graph homomorphism, Chordal graph, Computational complexity.
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/j.tcs.2010.05.041
OAI identifier: oai:dro.dur.ac.uk.OAI2:7419
Journal:

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