Topology

   

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.

Download: PDF

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

Unique-IP document downloads: 678 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus