On Counting Homomorphisms to Directed Acyclic Graphs

  • Martin Dyer
  • Leslie Ann Goldberg
  • Mike Paterson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


We give a dichotomy theorem for the problem of counting homomorphisms to directed acyclic graphs. H is a fixed directed acyclic graph. The problem is, given an input digraph G, to determine how many homomorphisms there are from G to H. We give a graph-theoretic classification, showing that for some digraphs H, the problem is in P and for the rest of the digraphs H the problem is #P-complete. An interesting feature of the dichotomy, absent from related dichotomy results, is the rich supply of tractable graphs H with complex structure.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Dyer
    • 1
  • Leslie Ann Goldberg
    • 2
  • Mike Paterson
    • 2
  1. 1.School of ComputingUniversity of LeedsLeedsUK
  2. 2.Dept. of Computer ScienceUniversity of WarwickCoventryUK

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