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The Chromatic Number of the Plane is at Least 5

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Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,197
I love this stuff! An amateur gets this one, though his result is refined by the pros. His paper on arXiv is here.
 

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,133
I love this stuff! An amateur gets this one, though his result is refined by the pros. His paper on arXiv is here.
Okay, why isn't the number four? Is this diagram of his not flat in the plane? I messed around with the 4 color theorem as a kid and I heard it was proved at some point. How is this one different?

-Dan
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,789
Okay, why isn't the number four? Is this diagram of his not flat in the plane? I messed around with the 4 color theorem as a kid and I heard it was proved at some point. How is this one different?

-Dan
The 4-color theorem is for coherent neighboring countries.
This is a more general theorem for graphs for which apparently 4 colors is not enough. We need at least 5 colors.