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Invariant colorings of random planar maps

Published online by Cambridge University Press:  22 April 2010

ÁDÁM TIMÁR
ÁDÁM TIMÁR*
Affiliation:
Hausdorff Center for Mathematics, Universität Bonn, D-53115 Bonn, Germany (email: adam.timar@hcm.uni-bonn.de)
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Abstract

We show that every locally finite random graph embedded in the plane with an isometry-invariant distribution can be five-colored in an invariant and deterministic way, under some non-triviality assumption and a mild assumption on the tail of edge lengths. The assumptions hold for any Voronoi map on a point process that has no non-trivial symmetries almost surely, hence we improve and generalize previous results on six-coloring the Voronoi map on a Poisson point process (see Angel, Benjamini, Gurel-Gurevich, Mayerovitch and Peled [Stationary map coloring. Preprint, 2008]).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 2 , April 2011 , pp. 549 - 562
Copyright
Copyright © Cambridge University Press 2010

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References

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