Vizing's theorem states that every simple undirected graph can be edge-colored using fewer than $Δ+ 1$ colors, where $Δ$ is the graph's maximum degree. The original proof was given through a polynomial-time algorithmic procedure that iteratively extends a partial coloring until it becomes complete. In this work, I used the Lean theorem prover to produce a verified implementation of the Misra and Gries edge-coloring algorithm, a modified version of Vizing's original method. The focus is on building libraries for relevant mathematical objects and rigorously maintaining required invariants.

翻译：Vizing定理表明，每个简单无向图可用少于$Δ+1$种颜色进行边着色，其中$Δ$为图的最大度数。原始证明通过多项式时间算法过程给出，该过程迭代扩展部分着色直至完成。本工作中，我使用Lean定理证明器实现了Misra与Gries边着色算法的验证版本，该算法是Vizing原始方法的改进形式。研究重点在于构建相关数学对象的程序库，并严格维护算法所需的不变性。