Three-coloring triangle-free graphs on surfaces I. Extending a coloring to a disk with one triangle

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10329888" target="_blank" >RIV/00216208:11320/16:10329888 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jctb.2016.04.003" target="_blank" >http://dx.doi.org/10.1016/j.jctb.2016.04.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2016.04.003" target="_blank" >10.1016/j.jctb.2016.04.003</a>

Result language
angličtina
Original language name
Three-coloring triangle-free graphs on surfaces I. Extending a coloring to a disk with one triangle
Original language description
Let G be a plane graph with exactly one triangle T and all other cycles of length at least 5, and let C be a facial cycle of G of length at most six. We prove that a 3-coloring of C does not extend to a 3-coloring of G if and only if C has length exactly six and there is a color x such that either G has an edge joining two vertices of C colored x, or T is disjoint from C and every vertex of T is adjacent to a vertex of C colored x. This is a lemma to be used in a future paper of this series.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

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

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