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Locally Constrained Homomorphisms on Graphs of Bounded Treewidth and Bounded Degree

  • Steven Chaplick
  • Jiří Fiala
  • Pim van ’t Hof
  • Daniël Paulusma
  • Marek Tesař
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8070)

Abstract

A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective, respectively. We prove that the problems of testing whether a given graph G allows a homomorphism to a given graph H that is locally bijective, surjective, or injective, respectively, are NP-complete, even when G has pathwidth at most 5, 4 or 2, respectively, or when both G and H have maximum degree 3. We complement these hardness results by showing that the three problems are polynomial-time solvable if G has bounded treewidth and in addition G or H has bounded maximum degree.

Keywords

Polynomial Time Maximum Degree Constraint Satisfaction Problem Tree Decomposition 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 2013

Authors and Affiliations

  • Steven Chaplick
    • 1
  • Jiří Fiala
    • 1
  • Pim van ’t Hof
    • 2
  • Daniël Paulusma
    • 3
  • Marek Tesař
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPragueCzech Republic
  2. 2.Department of InformaticsUniversity of BergenNorway
  3. 3.School of Engineering and Computing SciencesDurham UniversityUK

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