Computing vertex-surjective homomorphisms to partially reflexive trees

  • Authors:

  • Petr A. Golovach;Daniël Paulusma;Jian Song

  • Affiliations:

  • School of Engineering and Computing Sciences, Durham University, Science Laboratories, Durham, UK;School of Engineering and Computing Sciences, Durham University, Science Laboratories, Durham, UK;School of Engineering and Computing Sciences, Durham University, Science Laboratories, Durham, UK

  • Venue:
  • CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
  • Year:
  • 2011

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Abstract

A homomorphism from a graph G to a graph H is a vertex mapping f : VG → VH such that f(u) and f(v) form an edge in H whenever u and v form an edge in G. The H-Coloring problem is to test whether a graph G allows a homomorphism to a given graph H. A well-known result of Hell and Nešetřil determines the computational complexity of this problem for any fixed graph H. We study a natural variant of this problem, namely the SURJECTIVE H-COLORING problem, which is to test whether a graph G allows a homomorphism to a graph H that is (vertex-)surjective. We classify the computational complexity of this problem when H is any fixed partially reflexive tree. Thus we identify the first class of target graphs H for which the computational complexity of Surjective H-Coloring can be determined. For the polynomial-time solvable cases, we show a number of parameterized complexity results, especially on nowhere dense graph classes.