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17

FCT
2009
Springer

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Martingales on Trees and the Empire Chromatic Number of Random Trees

13 years 11 months ago

Martingales on Trees and the Empire Chromatic Number of Random Trees

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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.

Colin Cooper, Andrew R. A. McGrae, Michele Zito

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Dual Planar Graph | Empire Colouring Problem | FCT 2009 | Percy Heawood | Theoretical Computer Science |

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Added	26 May 2010
Updated	26 May 2010
Type	Conference
Year	2009
Where	FCT
Authors	Colin Cooper, Andrew R. A. McGrae, Michele Zito

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