Computational complexity of covering three-vertex multigraphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10331737" target="_blank" >RIV/00216208:11320/16:10331737 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1016/j.tcs.2015.09.013" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2015.09.013</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.tcs.2015.09.013" target="_blank" >10.1016/j.tcs.2015.09.013</a>

Result language

angličtina

Original language name

Computational complexity of covering three-vertex multigraphs

Original language description

A covering projection from a graph G onto a graph H is a mapping of the vertices of G onto the vertices of H such that, for every vertex v of G, the neighborhood of v is mapped bijectively onto the neighborhood of its image. Moreover, if G and H are multigraphs, then this local bijection has to preserve multiplicities of the neighbors as well. The notion of covering projection stems from topology, but has found applications in areas such as the theory of local computation and construction of highly symmetric graphs. It provides a restrictive variant of the constraint satisfaction problem with additional symmetry constraints on the behavior of the homomorphisms of the structures involved. We investigate the computational complexity of the problem of deciding the existence of a covering projection from an input graph G to a fixed target graph H. Among other partial results this problem has been shown NP-hard for simple regular graphs H of valency greater than 2, and a full characterization of computational complexity has been shown for target multigraphs with 2 vertices. We extend the previously known results to the ternary case, i.e., we give a full characterization of the computational complexity in the case of multigraphs with 3 vertices. We show that even in this case a P/NP-completeness dichotomy holds.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

IN - Informatics

OECD FORD branch

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Project

<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

—

Volume of the periodical

609

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

14

Pages from-to

104-117

UT code for WoS article

000367488400008

EID of the result in the Scopus database

2-s2.0-84948844353