par Dujmović, Vida V.;Frati, Fabrizio;Joret, Gwenaël ;Wood, David
Référence The electronic journal of combinatorics, 20, 1, P51
Publication Publié, 2013-03
Article révisé par les pairs
Résumé : A 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 sield. Despite this, the best known upper bound is O(√n) for n-vertex planar graphs. We prove a O(log n) upper bound.