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Towards a classical proof of the 4-colour theorem

Peter Dörre
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Abstract

It is easy to colour the subset of triangulations with minimum degree less than 5 by induction on the graph order n, whereas the case with minimum degree equal to 5 cannot be coloured by recolouring the neighbours of a single 5-valent vertex. Instead of trying to colour appropriate subgraphs composed of at least 5-valent vertices, the new strategy is to use the colouring information already provided by induction in a constructive way.

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Peter Dörre. 2004-08-27. Towards a classical proof of the 4-colour theorem. https://arxiv.org/abs/math/0408384

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