Asymptotically optimal frugal colouring

Authors:
Michael Molloy;Bruce Reed
Affiliations:
University of Toronto;McGill University and Projet Mascotte, CNRS-INRIA, Sophia-Antipolis, France
Venue:
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Year:
2009

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Abstract

We prove that every graph with maximum degree Δ can be properly (Δ + 1)-coloured so that no colour appears more than O(log Δ / log log Δ) times in the neighbourhood of any vertex. This is best possible up to the constant factor in the O(−) term. We also provide an efficient algorithm to produce such a colouring.