We study the first-order (FO) model checking problem of dense graph classes, namely, those that have FO interpretations in (or are FO transductions of) some sparse graph classes. We give a structural characterization of the graph classes that are FO interpretable in graphs of bounded degree. This characterization allows us to efficiently compute such an FO interpretation for an input graph. As a consequence, we obtain an FPT algorithm for successor-invariant FO model checking on any graph class that is FO interpretable in (or an FO transduction of) a graph class of bounded degree. The approach we use to obtain these results may also be of independent interest.

中文翻译：

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密集图类的 FO 模型检查新视角

我们研究了密集图类的一阶（FO）模型检查问题，即那些在一些稀疏图类中具有 FO 解释（或者是 FO 转导）的那些。我们给出了在有界度图中 FO 可解释的图类的结构特征。这种表征使我们能够有效地计算输入图的这种 FO 解释。因此，我们获得了一个 FPT 算法，用于检查任何在有界度图类中 FO 可解释（或 FO 转导）的图类的后继不变 FO 模型。我们用来获得这些结果的方法也可能具有独立的兴趣。