Martingales on trees and the empire chromatic number of random trees

Authors:
Colin Cooper;Andrew R. A. McGrae;Michele Zito
Affiliations:
Department of Computer Science, Kings' College, London, UK;Department of Computer Science, University of Liverpool, Liverpool, UK;Department of Computer Science, University of Liverpool, Liverpool, UK
Venue:
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Year:
2009

Citing 4
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Empires make cartography hard: the complexity of the empire colouring problem

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Abstract

We study the empire colouring problem (as defined by Percy Heawood in 1890) for maps whose dual planar graph is a tree, with empires formed by exactly r countries. We prove that, for each fixed r 1, with probability approaching one as the size of the graph grows to infinity, the minimum number of colours for which a feasible solution exists takes one of seven possible values.