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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 Tesar, M. (2013) 'Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree.', in Fundamentals of computation theory : 19th International Symposium, FCT 2013, 19-21 August 2013, Liverpool, UK ; proceedings. Berlin, Heidelberg: Springer, pp. 121-132. Lecture notes in computer science. (8070).


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:Book chapter
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Date accepted:No date available
Date deposited:14 January 2015
Date of first online publication:2013
Date first made open access:No date available

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