Irreducible 4-critical triangle-free toroidal graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10416989" target="_blank" >RIV/00216208:11320/20:10416989 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8j7G67UDlS" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8j7G67UDlS</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2020.103112" target="_blank" >10.1016/j.ejc.2020.103112</a>
Alternative languages
Result language
angličtina
Original language name
Irreducible 4-critical triangle-free toroidal graphs
Original language description
The theory of Dvorak, Kral', and Thomas (Dvorak, 2015) shows that a 4-critical triangle-free graph embedded in the torus has only a bounded number of faces of length greater than 4 and that the size of these faces is also bounded. We study the natural reduction in such embedded graphs-identification of opposite vertices in 4-faces. We give a computer-assisted argument showing that there are exactly four 4-critical triangle-free irreducible toroidal graphs in which this reduction cannot be applied without creating a triangle. Using this result, we show that every 4-critical triangle-free graph embedded in the torus has at most four 5-faces, or a 6-face and two 5-faces, or a 7face and a 5-face, in addition to at least seven 4-faces. This result serves as a basis for the exact description of 4-critical triangle-free toroidal graphs, which we present in a followup paper. (C) 2020 Elsevier Ltd. All rights reserved.
Czech name
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Czech description
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Classification
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
Result continuities
Project
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Continuities
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
Name of the periodical
European Journal of Combinatorics
ISSN
0195-6698
e-ISSN
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Volume of the periodical
88
Issue of the periodical within the volume
august
Country of publishing house
GB - UNITED KINGDOM
Number of pages
14
Pages from-to
103112
UT code for WoS article
000541875000011
EID of the result in the Scopus database
2-s2.0-85088517241