, Volume 79, Issue 3, pp 201-211

Gedanken zur Vier-Farben-Vermutung

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Abstract

It is shown that the four colour conjecture is equivalent to a conjecture on the existence of spanning Eulerian subgraphs of a certain type in triangulations of the plane. From this, a simple proof of Heawood's Equivalence Theorem is given. Moreover, an elementary operation is defined for triangulations of the plane; and by repeated application of this operation one can construct a given colouring from another given colouring.