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- W2572722231 abstract "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, Łuczak and Rödl: 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-Breaker game played on the vertices of $G$?" @default.
- W2572722231 created "2017-01-26" @default.
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- W2572722231 date "2013-04-17" @default.
- W2572722231 modified "2023-10-14" @default.
- W2572722231 title "The Biased Odd Cycle Game" @default.
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- W2572722231 doi "https://doi.org/10.37236/2819" @default.
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