透过逻辑的透镜看图类
Graph classes through the lens of logic
AI总结：
本综述以逻辑转导为基本嵌入机制，重新梳理经典结构图论概念，并介绍 monadic stability、monadic dependence 与结构稀疏图类等最新进展。
摘要：
逻辑中可定义的图变换可以使用转导（transductions）这一概念来描述。通过将转导理解为一种基本嵌入机制，它刻画了借助逻辑公式把一个图编码到另一个图中的可能性，我们获得了审视图类及其性质全貌的新视角。本综述旨在全面呈现结构图论中的这一角度。我们首先以逻辑为中心概述经典图论概念，例如 treedepth、shrubdepth、treewidth、cliquewidth、twin-width、有界扩张和无处稠密性。随后，我们介绍与完全通过转导定义的概念相关的最新进展，例如 monadic stability、monadic dependence，以及结构稀疏图类。
英文摘要：
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of logical formulas, we obtain a new perspective on the landscape of graph classes and of their properties. The aim of this survey is to give a comprehensive presentation of this angle on structural graph theory. We first give a logic-focused overview of classic graph-theoretic concepts, such as treedepth, shrubdepth, treewidth, cliquewidth, twin-width, bounded expansion, and nowhere denseness. Then, we present recent developments related to notions defined purely through transductions, such as monadic stability, monadic dependence, and classes of structurally sparse graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
