Map-Colour Theorems

Abstract

A map wil be calledk-chromatic or said to have chromatic numberkifkis the least positive integer having the property that the countries of the map can be divided intokmutually 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 forh> 1 the chromatic number of a map on a surface of connectivityhis at mostnh, where