The biased odd cycle Game

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F13%3A00209353" target="_blank" >RIV/68407700:21240/13:00209353 - isvavai.cz</a>
Result on the web
<a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i2p9" target="_blank" >http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i2p9</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
The biased odd cycle Game
Original language description
In this paper we consider biased Maker-Breaker games played on the edge set of a given graph $G$. We prove that for every $delta>0$ and large enough $n$, there exists a constant $k$ for which if $delta(G)geq delta n$ and $chi(G)geq k$, then Maker can build an odd cycle in the $(1:b)$ game for $b=Oleft(frac{n}{log^2 n}right)$. We also consider the analogous game where Maker and Breaker claim vertices instead of edges. This is a special case of the following well known and notoriously difficult problem due to Duffus, {L}uczak and R"{o}dl: is it true that for any positive constants $t$ and $b$, there exists an integer $k$ such that for every graph $G$, if $chi(G)geq k$, then Maker can build a graph which is not $t$-colorable, in the $(1:b)$ Maker-Breakergame played on the vertices of $G$?
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
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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