See this YouTube: Four Colour
It has to be untrue!
If I watched it before, same feeling.
It does not say that the areas would have to be continuous and we had trouble with the Maldives and Portugal colonized Brazil, so that they were once the same Country but they inhabited different continents, and things like that.
And the following reasoning:
That basically means create a hole in the yellow part, something like a tube connecting the boundary it makes with R1 and the third smaller rectangle.
This hole is still going to be R1. Yellow is still going to be yellow apart from the hole. Now we have it.
This hole is still going to be R1. Yellow is still going to be yellow apart from the hole. Now we have it.
We have just found a counter-example to the claim of the four-color theorem if my drawing satisfies the conditions of the theorem, and I think it does.
The four-colour theorem is not true therefore.
If the proof for five is correct, we should perhaps say five-colour theorem.
If the proof for five is correct, we should perhaps say five-colour theorem.
Send your thoughts to mrpprofessional@yahoo.com, please.
Final form, counter-example:
This paper seems to be a nice supplement for what we discuss in this blog post: http://article.sapub.org/10.5923.j.mijpam.20170101.03.html
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