Yet a short proof of the 4-colour theorem

Details Yet a short proof of the 4-colour theorem Yet a short proof of the 4-colour theorem

2004-08-27

arxiv.org/abs/math/0408384v21

Mathematics

Combinatorics

7 pages, 3 figures. Some text corrections in the first step of the proof. The second step is re-formulated as a counterexample

Scientific paper

The essential idea described in this paper is to use induction in order to prove for triangulations a sharper version of the 4-colour theorem: in addition to 4-colourability, the existence of a special colouring is claimed in which the special case (in terms of Kempe chains in the exterior of a 5-cycle) leading to the failure of Kempe's proof attempt does not exist. If this case is assumed to exist, a contradiction can be constructed in a surprisingly trivial way by using Jordan's curve theorem.

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