Complexity of planar signed graph homomorphisms to cycles

DROSS, Francois, Florent FOUCAUD, Valia MITSOU, Pascal OCHEM a Théo PIERRON. Complexity of planar signed graph homomorphisms to cycles. Discrete Applied Mathematics. 2020, roč. 284, 30 September 2020, s. 166-178. ISSN 0166-218X. Dostupné z: https://dx.doi.org/10.1016/j.dam.2020.03.029.

Základní údaje

Originální název

Complexity of planar signed graph homomorphisms to cycles

Autoři

DROSS, Francois, Florent FOUCAUD, Valia MITSOU, Pascal OCHEM a Théo PIERRON (250 Francie, garant, domácí)

Vydání

Discrete Applied Mathematics, 2020, 0166-218X

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Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.139

Kód RIV

RIV/00216224:14330/20:00118538

Organizační jednotka

Fakulta informatiky

DOI

http://dx.doi.org/10.1016/j.dam.2020.03.029

UT WoS

000543418800016

Klíčová slova anglicky

Signed graph; Edge-coloured graph; Graph homomorphism; Planar graph

Příznaky

Mezinárodní význam, Recenzováno

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Anotace

V originále

We study homomorphism problems of signed graphs from a computational point of view. A signed graph is an undirected graph where each edge is given a sign, positive or negative. An important concept when studying signed graphs is the operation of switching at a vertex, which is to change the sign of each incident edge. A homomorphism of a graph is a vertex-mapping that preserves the adjacencies; in the case of signed graphs, we also preserve the edge-signs. Special homomorphisms of signed graphs, called s-homomorphisms, have been studied. In an s-homomorphism, we allow, before the mapping, to perform any number of switchings on the source signed graph. The concept of s-homomorphisms has been extensively studied, and a full complexity classification (polynomial or NP-complete) for s-homomorphism to a fixed target signed graph has recently been obtained. Nevertheless, such a dichotomy is not known when we restrict the input graph to be planar, not even for non-signed graph homomorphisms. We show that deciding whether a (non-signed) planar graph admits a homomorphism to the square C-t(2) of a cycle with t >= 6, or to the circular clique K-4t(/()2t(-1)) with t >= 2, are NP-complete problems. We use these results to show that deciding whether a planar signed graph admits an s-homomorphism to an unbalanced even cycle is NP-complete. (A cycle is unbalanced if it has an odd number of negative edges). We deduce a complete complexity dichotomy for the planar s-homomorphism problem with any signed cycle as a target. We also study further restrictions involving the maximum degree and the girth of the input signed graph. We prove that planar s-homomorphism problems to signed cycles remain NP-complete even for inputs of maximum degree 3 (except for the case of unbalanced 4-cycles, for which we show this for maximum degree 4). We also show that for a given integer g, the problem for signed bipartite planar inputs of girth g is either trivial or NP-complete. (C) 2020 Published by Elsevier B.V.