(3a:a)-List-Colorability of Embedded Graphs of Girth at Least Five

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10416998" target="_blank" >RIV/00216208:11320/20:10416998 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=qbQNCkCI~_" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=qbQNCkCI~_</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/18M1214056" target="_blank" >10.1137/18M1214056</a>

Result language
angličtina
Original language name
(3a:a)-List-Colorability of Embedded Graphs of Girth at Least Five
Original language description
A graph G is list (b : a)-colorable if for every assignment of lists of size b to vertices of G there exists a choice of an a-element subset of the list at each vertex such that the subsets chosen at adjacent vertices are disjoint. We prove that for every positive integer a, the family of minimal obstructions of girth at least five to list (3a : a)-colorability is strongly hyperbolic, in the sense of the hyperbolicity theory developed by Postle and Thomas. This has a number of consequences; e.g., if a graph of girth at least five and Euler genus g is not list (3a : a)-colorable, then G contains a subgraph with O(g) vertices which is not list (3a : a)-colorable.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-04611S" target="_blank" >GA17-04611S: Ramsey-like aspects of graph coloring</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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