Geodesic
Planar graphs have bounded nonrepetitive chromatic number
Advances in Combinatorics (2020)

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arXiv
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.
Publié le : 
Vida Dujmović; Louis Esperet; Gwenaël Joret; Bartosz Walczak; David R. Wood. Planar graphs have bounded nonrepetitive chromatic number. Advances in Combinatorics (2020). http://geodesic.mathdoc.fr/item/ADVC_2020_a6/
@article{ADVC_2020_a6,
     author = {Vida Dujmovi\'c and Louis Esperet and Gwena\"el Joret and Bartosz Walczak and David R. Wood},
     title = {Planar graphs have bounded nonrepetitive chromatic number},
     journal = {Advances in Combinatorics},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2020_a6/}
}
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