Résumé
The Thue number$\pi(G)$of a graph$G$is the minimum number of colors needed to color$G$without creating a square on a path of$G$ . For a graph class$C$ ,$\pi(C)$is the supremum of$\pi(G)$over the graphs$G\in C$ . The Thue number has been investigated for famous minor-closed classes:$\pi(tree)=4$ ,$7\le\pi(outerplanar)\le12$ , and$11\le\pi(planar)\le768$ . Following a suggestion of Grytczuk, we consider the generalized parameters$\pi_k(C)$such that only squares of period at least$k$must be avoided. Thus,$\pi(C)=\pi_1(C)$ . We show that$\pi_5(tree)=2$ ,$\pi_2(tree)=3$ , and$\pi_k(planar)\ge11$for every fixed$k$ .