Computing Vertex-Surjective Homomorphisms to Partially Reflexive Trees

  • Petr A. Golovach
  • Daniël Paulusma
  • Jian Song
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6651)


A homomorphism from a graph G to a graph H is a vertex mapping f:V G  → V H 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.


Bipartite Graph Connected Graph Adjacent Vertex Graph Class Surjective Homomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Petr A. Golovach
    • 1
  • Daniël Paulusma
    • 1
  • Jian Song
    • 1
  1. 1.School of Engineering and Computing SciencesDurham University, Science LaboratoriesDurhamUK

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