Re: New proof of Four Color Theorem


anand_bheemaraju@xxxxxxxxx wrote:
> Hello Everyone, I am Anand , an undergraduate from India. I think I
> have stepped upon a new and simple proof of the Four color Theorem. I
> would like to submit it as a paper in some journals , but before I do
> that I would like to know whether the proof is a valid one or not and
> also whether the proof has been submitted already or not.
>
> you can find a copy of the proof at
> http://anandbh.cjb.cc/FOUR%20COLOR%20PROBLEM.pdf
>
> Any suggestions and replies are well appreciated.

Lots of people beat me to it, but I have one more complaint.

You can use your regularization to 4-color a planar graph with a loop
in it. However, any graph with a loop in it cannot be colored, even
with a large number of colors. So your proof must be wrong for this
reason (as well).

You're not giving Brooks enough credit here. That every graph is
(D+1)-colorable is obvious (where D is the maximum degree); use a
"greedy" coloring algorithm. Brooks's Theorem proper is that you can
use D colors unless:

(a) D = 2 and the graph contains an odd cycle (as a component); or
(b) D > 2 and the graph contains a K_D (as a component).

--- Christopher Heckman

.

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