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Academic Journal of Mathematical Sciences, 2020, 1(1); doi: 10.25236/AJMS.2020.010102.

Proof of four-color theorem of normal map


Jinhui Duan

Corresponding Author:
Jinhui Duan

Renmin University of China, Beijing, China


The four-color theorem, each map without enclaves can be colored with no more than four colors, but adjacent areas have different colors. In order to prove the four color theorem, I introduced a new concept primitive, base, power half ring, quotes the definition of kemp normal map and the other a conclusion: as long as proof of a normal map satisfy the four-color theorem, the other is normal maps and map is a map of meet the four-color theorem, namely he needed any so-called informal map to color generally smaller than the normal map.


The four-color theorem; normal map; primitive

Cite This Paper

Jinhui Duan. Proof of four-color theorem of normal map. Academic Journal of Mathematical Sciences (2020) Vol. 1 Issue 1: 8-13. https://doi.org/10.25236/AJMS.2020.010102.


[1] Kempe A B. On the Geographical Problem of the Four Colours[J]. American Journal of Mathematics, 1879, 2(3), page: 193-200.