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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.; Tesar, M.

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Authors

S. Chaplick

J. Fiala

van 't P. Hof

M. Tesar



Contributors

Leszek Gąsieniec
Editor

Frank Wolter
Editor

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., & Tesar, M. (2013). Locally Constrained Homomorphisms on Graphs of Bounded Treewidth and Bounded Degree. In L. Gąsieniec, & F. Wolter (Eds.), Fundamentals of computation theory : 19th International Symposium, FCT 2013, 19-21 August 2013, Liverpool, UK ; proceedings (121-132). https://doi.org/10.1007/978-3-642-40164-0_14

Conference Name Liverpool, UK
Conference Location 19th International Symposium, FCT 2013
Publication Date Jan 1, 2013
Deposit Date Dec 20, 2014
Publicly Available Date Jan 14, 2015
Pages 121-132
Series Title Lecture notes in computer science
Series Number 8070
Series ISSN 0302-9743,1611-3349
Book Title Fundamentals of computation theory : 19th International Symposium, FCT 2013, 19-21 August 2013, Liverpool, UK ; proceedings.
ISBN 9783642401633
DOI https://doi.org/10.1007/978-3-642-40164-0_14
Public URL https://durham-repository.worktribe.com/output/1153164

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