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A Pure Mathematical Proof of the 4-Colour Theorem

Author

Listed:
  • Jun Wang

    (Master Of Condensed Matter Physics of Sun Yat-Sen University, China)

Abstract

This work “A Pure Mathematical Proof of the 4-Colour Theorem†is related to the previous proof assited by computer. “Triangulations of Euler Convex Polygon†provides a fresh beginning point for the proof. The central concept is to discover an extended invariance property of Standard Graph’s boundary, which is described as “3-Colour All Phase States (3CP)†in this work and it is demonstrated that the Standard Graph’s boundary and sub-bound are 3CP and 4-colorable (4-3CP) via the Expanded Operation e(+, pi) and e(-, pi). It’s exciting that this regularity was discovered for the first time and the 4-3CP invariance can naturally derive the 4-Colour Theorem. The majority of the definitions, theorems and proof strategies are shown in this work.

Suggested Citation

  • Jun Wang, 2023. "A Pure Mathematical Proof of the 4-Colour Theorem," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 52(5), pages 44169-44176, September.
    • Handle: RePEc:abf:journl:v:52:y:2023:i:5:p:44169-44176
    DOI: 10.26717/BJSTR.2023.52.008323
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