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Nonrepetitive Colourings of Planar Graphs with O(log n) Colours
, 2012
"... A vertex colouring of a graph is nonrepetitive if there is no path for which the first half of the path is assigned the same sequence of colours as the second half. The nonrepetitive chromatic number of a graph G is the minimum integer k such that G has a nonrepetitive kcolouring. Whether planar gr ..."
Abstract

Cited by 6 (3 self)
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A vertex colouring of a graph is nonrepetitive if there is no path for which the first half of the path is assigned the same sequence of colours as the second half. The nonrepetitive chromatic number of a graph G is the minimum integer k such that G has a nonrepetitive kcolouring. Whether planar graphs have bounded nonrepetitive chromatic number is one of the most important open problems in the field. Despite this, the best known upper bound is O ( √ n) for nvertex planar graphs. We prove a O(log n) upper bound. 1