Map-Colour Theorems

Abstract

A map wil be called k -chromatic or said to have chromatic number k if k is the least positive integer having the property that the countries of the map can be divided into k mutually disjoint (colour) classes in such a way that no two countries which have a common frontier line are in the same (colour) class.Heawood [ 4 ] proved that for h > 1 the chromatic number of a map on a surface of connectivity h is at most n h , where