The Four Color Theorem and its aftermath

The Four Color Theorem is known to be one of the most famous results in graph theory. This theorem was proved by Appel and Haken in 1977, but the proof was computer-assisted to deal with about 2000 distinct cases. The statement of the Four Color Theorem is so simple, but its proof required the complicated arguments with computer. We consider whether we can persuade this situation, and give an explanation of the Four Color Theorem, introducing several results and notions derived from it, and moreover, recent developments related to it.

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Publication Details

Journal
Sugaku Expositions
Published
2025-11-25
DOI
https://doi.org/10.1090/suga/499
Primary Topic
Advanced Mathematical Theories
Type
article
Field-Weighted Citation Impact
0.00
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article

The Four Color Theorem and its aftermath

Atsuhiro Nakamoto, Kenta Ozeki
Sugaku Expositions
Advanced Mathematical Theories
article

The Four Color Theorem and its aftermath

Atsuhiro Nakamoto, Kenta Ozeki
article en

Abstract

The Four Color Theorem is known to be one of the most famous results in graph theory. This theorem was proved by Appel and Haken in 1977, but the proof was computer-assisted to deal with about 2000 distinct cases. The statement of the Four Color Theorem is so simple, but its proof required the complicated arguments with computer. We consider whether we can persuade this situation, and give an explanation of the Four Color Theorem, introducing several results and notions derived from it, and moreover, recent developments related to it.

Sugaku ExpositionsVol. 38(2)
Yokohama National University (JP)
Openalex Percentile: Top 58%
Advanced Mathematical Theories
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