Nonrepetitive colorings of graphs - A survey

Abstract

A vertex coloring f of a graph G is nonrepetitive if there are nointeger r ≥ 1 and a simple path v1, ..., v2r in G such that f(vi) = f(vr+i) for all i = 1, ..., r. This notion is a graph-theoretic variant of nonrepetitive sequences of Thue. The paper surveys problems and results on this topic.