Locally Injective Graph Homomorphism: Lists Guarantee Dichotomy

  • Jiří Fiala
  • Jan Kratochvíl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4271)


We prove that in the List version, the problem of deciding the existence of a locally injective homomorphism to a parameter graph H performs a full dichotomy. Namely we show that it is polynomially time solvable if every connected component of H has at most one cycle and NP-complete otherwise.


Connected Graph Constraint Satisfaction Problem Unary Relation Surjective Homomorphism Injective Homomorphism 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jiří Fiala
    • 1
  • Jan Kratochvíl
    • 1
  1. 1.Department of Applied Mathematics and, Institute for Theoretical Computer Science (ITI), Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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