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 The Four Color Theorem : a Jordan-free proof ?

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Posts : 95
Join date : 2009-09-15
Age : 55
Location : Alexandria

PostSubject: The Four Color Theorem : a Jordan-free proof ?   Thu Nov 12, 2009 2:58 pm

Hi fellows, look what I've just found at page 22 in this .pdf :

Theorem (the Jordan Curve Theorem for hypermaps):

A hypermap is planar iff it has no duplicate-free “Moebius contours” of the form :

A hypermap is something like this :

Of course, the previous two profs of the 4C theorem are Jordan free by default; here, it seems to me that the author replace all that topological stuff that some authors mention with his own definition: "As far as we know this is a new combinatorial definition of planarity."
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