Abstract Based on the algorithmic proof of Lovasz local lemma due to Moser and Tardos, Dujmovic et al. (2016) initiated the use of the so-called entropy compression method for graph coloring problems. Then, using the same approach Esperet and Parreau (2013) proved new upper bounds for several chromatic numbers, and explained how that approach could be used for many different coloring problems. Here, we follow this line of research for the particular case of acyclic coloring: we show that every graph with maximum degree Δ has acyclic chromatic number at most 3 2 Δ 4 3 + O ( Δ ) .

中文翻译：

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图的非循环着色和熵压缩方法

摘要 基于 Moser 和 Tardos 对 Lovasz 局部引理的算法证明，Dujmovic 等人。(2016) 开始使用所谓的熵压缩方法解决图着色问题。然后，使用相同的方法 Esperet 和 Parreau (2013) 证明了几个色数的新上限，并解释了该方法如何用于许多不同的着色问题。在这里，我们针对非循环着色的特殊情况遵循这一研究路线：我们表明，每个具有最大度数 Δ 的图都具有至多 3 2 Δ 4 3 + O (Δ ) 的非循环色数。