Mathematical Proof of Four Color Theorem

Authors: Liu Ran

The method and basic theory are far from traditional graph theory. Maybe they are the key factor of success. K4 regions (every region is adjacent to other 3 regions) are the max adjacent relationship, four-color theorem is true because more than 4 regions, there must be a non-adjacent region existing. Non-adjacent regions can be color by the same color and decrease color consumption. Another important three-color theorem is that the border of regions can be colored by 3 colors. Every region has at least 2 optional colors, which can be permuted.

Comments: 38 Pages.

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Submission history

[v1] 2013-06-22 12:52:13
[v2] 2013-06-23 10:58:19
[v3] 2013-06-24 10:24:04
[v4] 2013-07-03 10:48:17
[v5] 2013-07-13 11:04:12
[v6] 2013-07-16 08:35:28
[v7] 2013-07-16 09:50:57
[v8] 2013-07-18 10:30:04
[v9] 2013-07-25 10:39:27
[vA] 2013-07-27 10:49:06
[vB] 2013-07-27 21:41:36
[vC] 2013-07-29 10:00:10
[vD] 2013-09-03 08:53:52

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