Ein zum Vierfarbensatz Äquivalenter Satz der Panisochromie

A motivation for a partition of the four colour theorem into 11 cases is presented. Of these 11 cases we can exclude 9. The remaining pair of cases can be formulated as a property of certain planar 4-colourings. The property is called panisochromaticity. As far as I know there has been no studies of this concept for its own sake—at least not with respect to those aspects of interest for the four colour problem. The theme panisochromaticity also applies to graph colouring in general, e.g., to non-planar or infinite graphs. In the final part of this paper we exhibit a question on panisochromaticity equivalent to the four colour problem.