rocq-community/fourcolor

---

rocq-community/fourcolor.json

{
  "createdAt": "2018-11-06T17:43:35Z",
  "defaultBranch": "master",
  "description": "Formal proof of the Four Color Theorem [maintainer=@ybertot]",
  "fullName": "rocq-community/fourcolor",
  "homepage": "",
  "language": "Rocq Prover",
  "name": "fourcolor",
  "pushedAt": "2025-10-14T07:16:36Z",
  "stargazersCount": 223,
  "topics": [
    "coq",
    "coq-ci",
    "four-color-theorem",
    "mathcomp",
    "ssreflect"
  ],
  "updatedAt": "2025-11-20T08:10:39Z",
  "url": "https://github.com/rocq-community/fourcolor"
}

The Four Color Theorem

[![Docker CI][docker-action-shield]][docker-action-link] [![Contributing][contributing-shield]][contributing-link] [![Code of Conduct][conduct-shield]][conduct-link] [![Zulip][zulip-shield]][zulip-link]

[docker-action-shield] !: https://github.com/coq-community/fourcolor/actions/workflows/docker-action.yml/badge.svg?branch=master [docker-action-link] !: https://github.com/coq-community/fourcolor/actions/workflows/docker-action.yml

[contributing-shield] !: https://img.shields.io/badge/contributions-welcome-%23f7931e.svg [contributing-link] !: https://github.com/coq-community/manifesto/blob/master/CONTRIBUTING.md

[conduct-shield] !: https://img.shields.io/badge/%E2%9D%A4-code%20of%20conduct-%23f15a24.svg [conduct-link] !: https://github.com/coq-community/manifesto/blob/master/CODE_OF_CONDUCT.md

[zulip-shield] !: https://img.shields.io/badge/chat-on%20zulip-%23c1272d.svg [zulip-link] !: https://coq.zulipchat.com/#narrow/stream/237663-coq-community-devs.20.26.20users

This library contains a formal proof of the Four Color Theorem in Coq, along with the theories needed to support stating and then proving the Theorem. This includes an axiomatization of the setoid of classical real numbers, basic plane topology definitions, and a theory of combinatorial hypermaps.

Meta

• Author(s):
  • Georges Gonthier (initial)
• Coq-community maintainer(s):
  • Yves Bertot (@ybertot)
• License: [CeCILL-B]!(LICENSE)
• Compatible Coq versions: 8.20 or later
• Additional dependencies:
  • MathComp ssreflect 2.5.0 or later
  • MathComp algebra
  • Hierarchy Builder 1.5.0 or later
• Coq namespace: fourcolor
• Related publication(s):
  • Formal Proof—The Four-Color Theorem
  • A computer-checked proof of the Four Color Theorem

Building and installation instructions

The easiest way to install the latest released version of The Four Color Theorem is via opam:

opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-fourcolor

If you are only interested in the formalization of real numbers, you can install it separately:

opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-fourcolor-reals

To instead build and install the whole project manually from the repository, do:

git clone https://github.com/coq-community/fourcolor.git
cd fourcolor
make   # or make -j <number-of-cores-on-your-machine>
make install

Documentation

The Four Color Theorem (Appel & Haken, 1976) is a landmark result of graph theory.

The formal proof is based on the Mathematical Components library.