Szemerédi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich combinatorial context. In particular, we stress the link to the theory of (structural) sparsity, which leads to alternative proofs, refinements and solutions of open problems. It is interesting to note that many of these classes present challenging problems. Nevertheless, from the point of view of regularity lemma type statements, they appear as ``gentle'' classes.

中文翻译：

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温和图的规则分区

Szemerédi 的正则引理是一个非常有用的极值组合工具。最近，针对特殊的、更结构化的图类获得了对这一开创性结果的一些改进。我们在丰富的组合背景下调查这些结果。我们特别强调了与（结构）稀疏性理论的联系，这导致了开放问题的替代证明、改进和解决方案。有趣的是，其中许多类都存在具有挑战性的问题。然而，从正则性引理类型陈述的角度来看，它们表现为“温和”类。