EKR 定理是图论中的一个重要定理，由 Erd? s，柯召和Rado 最早提出并证明。此后又有学者提出了各种不同的证明方法。这篇文章首先介绍了图论和有限集族的基本概念。EKR 定理讨论的是图论中关于有限集族的基数问题。文章阐述了 EKR 定理提出的背景以及定理的内容和最原始的证明过程。在此之后，文章梳理了两种更为简短的组合证明方法，考察了这些方法相互间的对比。另外，文章又分别介绍了一种代数证明方法和一种概率证明方法。

EKR Theorem is an important part in GRAPH THEORY.Erd?s, Ko and Rado came up with the theorem and a proof at first place.From then on, some other scholars came up with different ways to prove the theorem. This article first introduced some basic concepts about GRAPH THEORY and family of finite sets. EKR Theorem deals with the problem about the cardinality of a family of finite sets. This article shows how EKR Theorem is formed and its definition and original proof by Erd?s, Ko and Rado. After that, this article goes with two other shorter proofs with Combination method and makes a comparison among them. Then, here are two proofs, which are separately with Algebra method and Probability method.