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

Authors:
Andrew R. A. McGrae;Michele Zito
Affiliations:
Department of Computer Science, University of Liverpool, Liverpool, UK;Department of Computer Science, University of Liverpool, Liverpool, UK
Venue:
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2011

Citing 4
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Abstract

We study the empire colouring problem (as defined by Percy Heawood in 1890) for maps containing empires formed by exactly r1 countries each. We prove that the problem can be solved in polynomial time using s colours on maps whose underlying adjacency graph has no induced subgraph of average degree larger than s/r. However, if s≥3, the problem is NP-hard for forests of paths of arbitrary lengths (if s