TY - JOUR
T1 - Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree
AU - Chaplick, Steven
AU - Fiala, Jirí
AU - Hof, Pim van 't
AU - Paulusma, Daniël
AU - Tesar, Marek
N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2015
Y1 - 2015
N2 - 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. (C) 2015 Elsevier B.V. All rights reserved.
AB - 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. (C) 2015 Elsevier B.V. All rights reserved.
U2 - 10.1016/J.TCS.2015.01.028
DO - 10.1016/J.TCS.2015.01.028
M3 - Article
SN - 0304-3975
VL - 590
SP - 86
EP - 95
JO - Theoretical Computer Science
JF - Theoretical Computer Science
ER -