标题： 计算机辅助图论：综述 显示英文标题

标题： Computer-assisted graph theory: a survey

摘要： 计算机和算法在获得图论新结果中的作用正变得越来越重要。 在本综述中，我们介绍了用于计算机辅助图论的各种技术，包括在一个给定类别内生成所有成对非同构图的穷举生成方法，使用包含图和不变量的可搜索数据库，以及其他已确立和新兴的算法范式。 我们涵盖了基于混合整数线性规划、半定规划、动态规划、SAT求解、元启发式和机器学习的方法。 这些技术通过大量详细的结果进行了说明，涵盖了图论的几个重要子领域，如极值图论、图着色、结构图论、谱图论、正则图、拓扑图论、图中的特殊集合、代数图论和化学图论。 我们还介绍了一些较小的新结果，这些结果展示了在开发了适当的工具后，计算机辅助图论方法可以多么容易地被应用。 显示英文摘要

摘要： Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all pairwise non-isomorphic graphs within a given class, the use of searchable databases containing graphs and invariants as well as other established and emerging algorithmic paradigms. We cover approaches based on mixed integer linear programming, semidefinite programming, dynamic programming, SAT solving, metaheuristics and machine learning. The techniques are illustrated with numerous detailed results covering several important subareas of graph theory such as extremal graph theory, graph coloring, structural graph theory, spectral graph theory, regular graphs, topological graph theory, special sets in graphs, algebraic graph theory and chemical graph theory. We also present some smaller new results that demonstrate how readily a computer-assisted graph theory approach can be applied once the appropriate tools have been developed.