关于Kuratowski图的平面性判据
On the Kuratowski graph planarity criterion
摘要：
这篇论文纯粹是阐述性的。Kuratowski图平面性准则的陈述是简单且众所周知的。然而，它的经典证明并不容易。在本文中，我们提出了Makarychev证明（进一步简化Prasolov，Telishev，Zaslavski和作者），这可能是最简单的。在俄罗斯版本之前的证明，我们提出了所有必要的定义，之后，我们国家的一些密切的结果图和更一般的空间。这篇论文是为学生熟悉的概念图，并可能是一个有趣的容易阅读成熟的数学家。
英文摘要：
This paper is purely expositional. The statement of the Kuratowski graph planarity criterion is simple and well-known. However, its classical proof is not easy. In this paper we present the Makarychev proof (with further simplifications by Prasolov, Telishev, Zaslavski and the author) which is possibly the simplest. In the Rusian version before the proof we present all the necessary definitions, and afterwards we state some close results on graphs and more general spaces. The paper is accessible for students familiar with the notion of a graph, and could be an interesting easy reading for mature mathematicians.
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。
