Towards a classical proof of the 4-colour theorem

2004/08/27 by Peter Dörre, Dörre, Peter
#math.GM

paper · pdf · doi:10.48550/arxiv.math/0408384

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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