2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 133134
author:  Noga Alon and Jarosław Grytczuk 

title:  Nonrepetitive colorings of graphs 
keywords:  
abstract: 
A vertex coloring of a graph
G
is
k
nonrepetitive if one cannot find a periodic
sequence with
k
blocks on any simple path of
G
. The minimum number of colors needed for such
coloring is denoted by
π
. This idea combines graph colorings with Thue
sequences introduced at the beginning of 20th century. In
particular Thue proved that if
k
(G)
G
is a simple path of any length greater than 4 then
π
and
2
(G)=3
π
. We investigate
3
(G)=2
π
for other classes of graphs. Particularly interesting
open problem is to decide if there is, possibly huge,
k
(G)
k
such that
π
is bounded for planar graphs.
k
(G)

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reference:  Noga Alon and Jarosław Grytczuk (2005), Nonrepetitive colorings of graphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 133134 
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