Characterization of 4-critical triangle-free toroidal graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10448429" target="_blank" >RIV/00216208:11320/22:10448429 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=fWiiPgl8.m" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=fWiiPgl8.m</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2022.01.008" target="_blank" >10.1016/j.jctb.2022.01.008</a>

Result language
angličtina
Original language name
Characterization of 4-critical triangle-free toroidal graphs
Original language description
We give an exact characterization of 3-colorability of triangle free graphs drawn in the torus, in the form of 186 "templates" (graphs with certain faces filled by arbitrary quadrangulations) such that a graph from this class is not 3-colorable if and only if it contains a subgraph matching one of the templates. As a consequence, we show every triangle-free graph drawn in the torus with edge-width at least six is 3-colorable, a key property used in an efficient 3-colorability algorithm for triangle-free toroidal graphs. (c) 2022 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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