5-list-coloring planar graphs with distant precolored vertices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10364949" target="_blank" >RIV/00216208:11320/17:10364949 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jctb.2016.06.006" target="_blank" >http://dx.doi.org/10.1016/j.jctb.2016.06.006</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2016.06.006" target="_blank" >10.1016/j.jctb.2016.06.006</a>

Result language
angličtina
Original language name
5-list-coloring planar graphs with distant precolored vertices
Original language description
We answer positively the question of Albertson asking whether every planar graph can be 5-list-colored even if it contains precolored vertices, as long as they are sufficiently far apart from each other. In order to prove this claim, we also give bounds on the sizes of graphs critical with respect to 5-list coloring. In particular, if G is a planar graph, H is a connected subgraph of G and L is an assignment of lists of colors to the vertices of G such that vertical bar L(v)vertical bar >= 5 for every v is an element of V(G)V(H) and G is not L-colorable, then G contains a subgraph with O(vertical bar H vertical bar(2)) vertices that is not L-colorable.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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