Locally Constrained Homomorphisms on Graphs of Bounded Treewidth and Bounded Degree
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.
Keywords
Cite
@article{arxiv.1408.6676,
title = {Locally Constrained Homomorphisms on Graphs of Bounded Treewidth and Bounded Degree},
author = {Steven Chaplick and Jiří Fiala and Pim van 't Hof and Daniël Paulusma and Marek Tesař},
journal= {arXiv preprint arXiv:1408.6676},
year = {2015}
}
Comments
An extended abstract of this paper appeared in the proceedings of FCT 2013, LNCS 8070: 121-132. http://dx.doi.org/10.1007/978-3-642-40164-0_14