### 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 -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.

Original language | English |
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Pages (from-to) | 173-188 |

Number of pages | 16 |

Journal | Journal of discrete algorithms |

Volume | 14 |

DOIs | |

Publication status | Published - 2012 |

Externally published | Yes |

Event | 21st International Workshop on Combinatorial Algorithms, IWOCA 2010 - London, United Kingdom Duration: 26 Jul 2010 → 28 Jul 2010 Conference number: 21 |

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## Cite this

Heggernes, P., van 't Hof, P., & Paulusma, D. (2012). Computing role assignments of proper interval graphs in polynomial time.

*Journal of discrete algorithms*,*14*, 173-188. https://doi.org/10.1016/j.jda.2011.12.004