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Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree.

Chaplick, S. and Fiala, J. and Hof, van 't P. and Paulusma, D. and Tesař, M. (2015) 'Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree.', Theoretical computer science., 590 . pp. 86-95.


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.

Item Type:Article
Keywords:Computational complexity, Locally constrained graph homomorphisms, Bounded treewidth, Bounded degree.
Full text:(AM) Accepted Manuscript
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Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Theoretical computer science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical computer science, 590, 26 July 2015, 10.1016/j.tcs.2015.01.028
Date accepted:16 January 2015
Date deposited:25 January 2015
Date of first online publication:July 2015
Date first made open access:No date available

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