Abstract Szemeredi's regularity lemma is one instance in a family of regularity lemmas, replacing the definition of density of a graph by a more general coefficient. Recently, Fan Chung proved another instance, a regularity lemma for clustering graphs, and asked whether good upper bounds could be derived for the quantitative estimates it supplies. We answer this question in the negative, for every generalized regularity lemma.

中文翻译：

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对聚类图的正则性引理的限制

摘要 Szemeredi 的正则性引理是正则性引理族中的一个实例，用更一般的系数代替了图的密度定义。最近，Fan Chung 证明了另一个例子，聚类图的正则性引理，并询问是否可以为它提供的定量估计推导出好的上限。对于每个广义正则性引理，我们都否定地回答这个问题。