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Planar graphs have bounded nonrepetitive chromatic number
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A colouring of a graph is "nonrepetitive" if for every path of even order, the sequence of colours on the first half of the path is different from the sequence of colours on the second half. We show that planar graphs have nonrepetitive colourings with a bounded number of colours, thus proving a conjecture of Alon, Grytczuk, Haluszczak and Riordan (2002). We also generalise this result for graphs of bounded Euler genus, graphs excluding a fixed minor, and graphs excluding a fixed topological minor.
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Cited by 2 Pith papers
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Shorter Labeling Schemes for Planar Graphs
Every n-vertex planar graph admits an adjacency labeling scheme with labels of length (4/3+o(1)) log n, improving the previous (2+o(1)) log n bound.
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A note about online nonrepetitive coloring $k$-trees
Every k-tree and partial k-tree admits an online nonrepetitive coloring with 4^k colors, and online paths need only 12 colors.
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