The biased odd cycle Game

Kód výsledku v 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>

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

The biased odd cycle Game

Popis výsledku v původním jazyce

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 $G$?

Název v anglickém jazyce

The biased odd cycle Game

Popis výsledku anglicky

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 $G$?

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Journal of Combinatorics (E-JC),

ISSN

1077-8926

e-ISSN

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Svazek periodika

20

Číslo periodika v rámci svazku

20(2)

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

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Kód UT WoS článku

000317564000001

EID výsledku v databázi Scopus

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