Computing role assignments of proper interval graphs in polynomial time

  • Authors:

  • Pinar Heggernes;Pim van t Hof;Daniël Paulusma

  • Affiliations:

  • Department of Informatics, University of Bergen, P.O. Box 7803, N-5020 Bergen, Norway;Department of Informatics, University of Bergen, P.O. Box 7803, N-5020 Bergen, Norway;School of Engineering and Computing Sciences, Durham University, Science Laboratories, South Road, Durham DH1 3LE, England, United Kingdom

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2012

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Abstract

An R-role assignment of a graph G is a locally surjective homomorphism from G to graph R. For a fixed graph R, the R-Role Assignment problem is to decide, for an input graph G, whether G has an R-role assignment. When both graphs G and R are given as input, the problem is called Role Assignment. In this paper, we study the latter problem. It is known that R-Role Assignment is NP-complete already when R is a path on three vertices. In order to obtain polynomial time algorithms for Role Assignment, it is therefore necessary to put restrictions on G. So far, the only known non-trivial case for which this problem is solvable in polynomial time is when G is a tree. We present an algorithm that solves Role Assignment in polynomial time when G is a proper interval graph. Thus we identify the first graph class other than trees on which the problem is tractable. As a complementary result, we show that Role Assignment is Graph Isomorphism-hard on chordal graphs, a superclass of proper interval graphs and trees.