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arXiv · 2512.13999

A verified implementation of the Misra and Gries edge coloring algorithm

Arohee Bhoja
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Abstract

Vizing's theorem states that every simple undirected graph can be edge-colored using fewer than $\Delta + 1$ colors, where $\Delta$ 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.

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Arohee Bhoja. 2025-12-16. A verified implementation of the Misra and Gries edge coloring algorithm. https://arxiv.org/abs/2512.13999

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