Nonrepetitive colorings of graphs

Noga Alon 1 Jaroslaw Grytczuk 2
1 Raymond and Beverly Sackler Faculty of Exact Sciences
2 Faculty of Mathematics, Computer Science and Econometric [Zielona Góra]
Abstract : A vertex coloring of a graph $G$ is $k \textit{-nonrepetitive}$ 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 $\pi _k(G)$ . This idea combines graph colorings with Thue sequences introduced at the beginning of 20th century. In particular Thue proved that if $G$ is a simple path of any length greater than $4$ then $\pi _2(G)=3$ and $\pi_3(G)=2$. We investigate $\pi_k(G)$ for other classes of graphs. Particularly interesting open problem is to decide if there is, possibly huge, $k$ such that $\pi_k(G)$ is bounded for planar graphs.
Keywords : nonrepetitive graph coloring Thue sequences planar graphs
Type de document :
Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.133-134, 2005, DMTCS Proceedings
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Noga Alon, Jaroslaw Grytczuk. Nonrepetitive colorings of graphs. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.133-134, 2005, DMTCS Proceedings. 〈hal-01184372〉

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