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Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree

Chaplick, S.; Fiala, J.; Hof, van 't P.; Paulusma, D.; Tesař, M.

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Authors

S. Chaplick

J. Fiala

van 't P. Hof

M. Tesař



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.

Citation

Chaplick, S., Fiala, J., Hof, V. '. P., Paulusma, D., & Tesař, M. (2015). Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree. Theoretical Computer Science, 590, 86-95. https://doi.org/10.1016/j.tcs.2015.01.028

Journal Article Type Article
Acceptance Date Jan 16, 2015
Publication Date Jul 26, 2015
Deposit Date Jan 23, 2015
Publicly Available Date Jan 25, 2015
Journal Theoretical Computer Science
Print ISSN 0304-3975
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 590
Pages 86-95
DOI https://doi.org/10.1016/j.tcs.2015.01.028
Keywords Computational complexity, Locally constrained graph homomorphisms, Bounded treewidth, Bounded degree.
Public URL https://durham-repository.worktribe.com/output/1413802

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Copyright 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





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