Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Keeping Avoider's graph almost acyclic   We consider biased $(1:b)$ Avoider-Enforcer games in the monotone and strict
versions. In particular, we show that Avoider can keep his graph being a forest
for every but maybe the last round of the game if $b \geq 200 n \ln n$. By this
we obtain essentially optimal upper bounds on the threshold biases for the
non-planarity game, the non-$k$-colorability game, and the $K_t$-minor game
thus addressing a question and improving the results of Hefetz, Krivelevich,
Stojakovi\'c, and Szab\'o. Moreover, we give a slight improvement for the lower
bound in the non-planarity game.

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The categories of this paper are: econ
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The categories of this paper are: eess
29
The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int