Irreducible 4-critical triangle-free toroidal graphs

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Irreducible 4-critical triangle-free toroidal graphs

Popis výsledku v původním jazyce

The theory of Dvorak, Kral&apos;, 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.

Název v anglickém jazyce

Irreducible 4-critical triangle-free toroidal graphs

Popis výsledku anglicky

The theory of Dvorak, Kral&apos;, 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

European Journal of Combinatorics

ISSN

0195-6698

e-ISSN

—

Svazek periodika

88

Číslo periodika v rámci svazku

august

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

14

Strana od-do

103112

Kód UT WoS článku

000541875000011

EID výsledku v databázi Scopus

2-s2.0-85088517241