Add to ORKGA 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 k-colouring. 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 n-vertex planar graphs. We prove a O(log n) upper bound.
A vertex colouring of a graph is nonrepetitive if there is no path whose first half receives the sam...
A vertex colouring of a graph is nonrepetitive if there is no path whose first half receives the sam...
A vertex coloring f of a graph G is nonrepetitive if there are no integer r ≥ 1 and a simple path v1...
A vertex colouring of a graph is nonrepetitive if there is no path for which the first half of the p...
A vertex colouring of a graph is nonrepetitive if there is no path for which the first half of the p...
A vertex colouring of a graph is nonrepetitive if there is no path for which the first half of the p...
A colouring of a graph is "nonrepetitive" if for every path of even order, the sequence of colours o...
International audienceA colouring of a graph is "nonrepetitive" if for every path of even order, the...
We prove that graphs excluding a fixed immersion have bounded nonrepetitive chromatic number. More g...
The following seemingly simple question with surprisingly many connections to various problems in co...
We prove that the facial nonrepetitive chromatic number of any outerplanar graph is at most 11 and o...
A sequence S = s1s2:::s2n is called a repetition if si = sn+i for each i = 1;:::; n. A coloring of t...
A vertex coloring of a graph $G$ is $k \textit{-nonrepetitive}$ if one cannot find a periodic sequen...
AbstractA coloring of a graph is nonrepetitive if the graph contains no path that has a color patter...
We consider the problem of coloring a planar graph with the minimum number of colors such that each ...
A vertex colouring of a graph is nonrepetitive if there is no path whose first half receives the sam...
A vertex colouring of a graph is nonrepetitive if there is no path whose first half receives the sam...
A vertex coloring f of a graph G is nonrepetitive if there are no integer r ≥ 1 and a simple path v1...
A vertex colouring of a graph is nonrepetitive if there is no path for which the first half of the p...
A vertex colouring of a graph is nonrepetitive if there is no path for which the first half of the p...
A vertex colouring of a graph is nonrepetitive if there is no path for which the first half of the p...
A colouring of a graph is "nonrepetitive" if for every path of even order, the sequence of colours o...
International audienceA colouring of a graph is "nonrepetitive" if for every path of even order, the...
We prove that graphs excluding a fixed immersion have bounded nonrepetitive chromatic number. More g...
The following seemingly simple question with surprisingly many connections to various problems in co...
We prove that the facial nonrepetitive chromatic number of any outerplanar graph is at most 11 and o...
A sequence S = s1s2:::s2n is called a repetition if si = sn+i for each i = 1;:::; n. A coloring of t...
A vertex coloring of a graph $G$ is $k \textit{-nonrepetitive}$ if one cannot find a periodic sequen...
AbstractA coloring of a graph is nonrepetitive if the graph contains no path that has a color patter...
We consider the problem of coloring a planar graph with the minimum number of colors such that each ...
A vertex colouring of a graph is nonrepetitive if there is no path whose first half receives the sam...
A vertex colouring of a graph is nonrepetitive if there is no path whose first half receives the sam...
A vertex coloring f of a graph G is nonrepetitive if there are no integer r ≥ 1 and a simple path v1...