List Homomorphism Problems for Signed Graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422005" target="_blank" >RIV/00216208:11320/20:10422005 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.MFCS.2020.20" target="_blank" >https://doi.org/10.4230/LIPIcs.MFCS.2020.20</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2020.20" target="_blank" >10.4230/LIPIcs.MFCS.2020.20</a>
Alternative languages
Result language
angličtina
Original language name
List Homomorphism Problems for Signed Graphs
Original language description
We consider homomorphisms of signed graphs from a computational perspective. In particular, we study the list homomorphism problem seeking a homomorphism of an input signed graph (G,σ), equipped with lists L(v) SUBSET OF OR EQUAL TO V(H), v ELEMENT OF V(G), of allowed images, to a fixed target signed graph (H,π). The complexity of the similar homomorphism problem without lists (corresponding to all lists being L(v) = V(H)) has been previously classified by Brewster and Siggers, but the list version remains open and appears difficult. Both versions (with lists or without lists) can be formulated as constraint satisfaction problems, and hence enjoy the algebraic dichotomy classification recently verified by Bulatov and Zhuk. By contrast, we seek a combinatorial classification for the list version, akin to the combinatorial classification for the version without lists completed by Brewster and Siggers. We illustrate the possible complications by classifying the complexity of the list homomorphism problem when H is a (reflexive or irreflexive) signed tree. It turns out that the problems are polynomial-time solvable for certain caterpillar-like trees, and are NP-complete otherwise. The tools we develop will be useful for classifications of other classes of signed graphs, and we mention some follow-up research of this kind; those classifications are surprisingly complex.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
ISBN
978-3-95977-159-7
ISSN
1868-8969
e-ISSN
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Number of pages
14
Pages from-to
1-14
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum f{"u}r Informatik
Place of publication
Dagsthul, Německo
Event location
online
Event date
Aug 24, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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