List Colorings with Distinct List Sizes, the Case of Complete Bipartite Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10332568" target="_blank" >RIV/00216208:11320/16:10332568 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/jgt.21896" target="_blank" >http://dx.doi.org/10.1002/jgt.21896</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.21896" target="_blank" >10.1002/jgt.21896</a>

Result language
angličtina
Original language name
List Colorings with Distinct List Sizes, the Case of Complete Bipartite Graphs
Original language description
Let $f:V rightarrow mathbb{N}$ be a function on the vertex set of the graph $G=(V,E)$. The graph $G$ is {em $f$-choosable} if for every collection of lists with list sizes specified by $f$ there is a proper coloring using colors from the lists. The sum choice number, $chi_{sc}(G)$, is the minimum of $sum f(v)$, over all functions $f$ such that $G$ is $f$-choosable. It is known (Alon 1993, 2000) that if $G$ has average degree $d$, then the usual choice number $chi_ell(G)$ is at least $Omega(log d)$, so they grow simultaneously. In this paper we show that $chi_{sc}(G)/|V(G)|$ can be bounded while the minimum degree $delta_{min}(G)rightarrow infty$. Our main tool is to give tight estimates for the sum choice number of the unbalanced complete bipartite graph $K_{a,q}$.
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/GPP201%2F12%2FP288" target="_blank" >GPP201/12/P288: Graph representations</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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