Paper
A verified implementation of the Misra and Gries edge coloring algorithm
Authors
Arohee Bhoja
Abstract
Vizing's theorem states that every simple undirected graph can be edge-colored using fewer than colors, where 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.