Locally Constrained Homomorphisms on Graphs of Bounded Treewidth and Bounded Degree

Steven Chaplick, Jirí Fiala, Pim van 't Hof, Daniël Paulusma, Marek Tesar

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


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.keywordspolynomial timemaximum degreeconstraint satisfaction problemtree decompositionsurjective homomorphismthese 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.
Original languageEnglish
Title of host publicationFundamentals of Computation Theory. FCT 2013
PublisherSpringer, Berlin, Heidelberg
Publication statusPublished - 2013
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science


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