The Four Color Theorem: A Constructive Proof and a Coloring Algorithm

In this version, the proof has become shorter and, in our view, clearer. The proof is now based on a single mechanism — the forced chain. K₄ and odd stars are treated as special cases of this mechanism. A demonstration of the algorithm has also been added, showing how it sequentially finds forced chains, splits edges, and arrives at a 4-coloring.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-23
DOI
https://doi.org/10.5281/zenodo.21514884
Primary Topic
Advanced Mathematical Theories
Type
preprint
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preprint

The Four Color Theorem: A Constructive Proof and a Coloring Algorithm

Vasilii Kostin
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories
preprint

The Four Color Theorem: A Constructive Proof and a Coloring Algorithm

Vasilii Kostin
preprint en

Abstract

In this version, the proof has become shorter and, in our view, clearer. The proof is now based on a single mechanism — the forced chain. K₄ and odd stars are treated as special cases of this mechanism. A demonstration of the algorithm has also been added, showing how it sequentially finds forced chains, splits edges, and arrives at a 4-coloring.

Zenodo (CERN European Organization for Nuclear Research)
Independent University of Moscow (RU)
Advanced Mathematical Theories
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