%0 Journal Article
%T Empire Maps on Surfaces
%A Caspar de Haes
%J Mathematics
%D 2011
%I arXiv
%X This report is an introduction to mathematical map colouring and the problems posed by Heawood in his paper of 1890. There will be a brief discussion of the Map Colour Theorem; then we will move towards investigating empire maps in the plane and the recent contributions by Wessel. Finally we will conclude with a discussion of all known results for empire maps on higher genus surfaces and prove Heawoods Empire Conjecture in a previously unknown case.
%U http://arxiv.org/abs/1106.4235v1