Geodesic
Planar graphs have bounded nonrepetitive chromatic number
Advances in Combinatorics (2020)
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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.
Publié le : 
@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/}
}
TY  - JOUR
AU  - Vida Dujmović
AU  - Louis Esperet
AU  - Gwenaël Joret
AU  - Bartosz Walczak
AU  - David R. Wood
TI  - Planar graphs have bounded nonrepetitive chromatic number
JO  - Advances in Combinatorics
PY  - 2020
UR  - http://geodesic.mathdoc.fr/item/ADVC_2020_a6/
LA  - en
ID  - ADVC_2020_a6
ER  - 
%0 Journal Article
%A Vida Dujmović
%A Louis Esperet
%A Gwenaël Joret
%A Bartosz Walczak
%A David R. Wood
%T Planar graphs have bounded nonrepetitive chromatic number
%J Advances in Combinatorics
%D 2020
%U http://geodesic.mathdoc.fr/item/ADVC_2020_a6/
%G en
%F ADVC_2020_a6
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/