Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree

  • Authors:

  • Steven Chaplick;Jiří Fiala;Pim van 't Hof;Daniël Paulusma;Marek Tesař

  • Affiliations:

  • Department of Applied Mathematics, Charles University, Prague, Czech Republic;Department of Applied Mathematics, Charles University, Prague, Czech Republic;Department of Informatics, University of Bergen, Norway;School of Engineering and Computing Sciences, Durham University, UK;Department of Applied Mathematics, Charles University, Prague, Czech Republic

  • Venue:
  • FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

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.