In a symmetric graph, a deterministic distributed algorithm cannot find a proper vertex coloring. Some auxiliary information is needed in order to break symmetry. A standard assumption is that initially each node has a "unique identifier", for example, from the set {1, 2, ..., "n"}. Put otherwise, we assume that we are given an "n"-coloring. The challenge is to "reduce" the number of colors from "n" to, e.g., Δ + 1. The more colors are employed, e.g. O(Δ) instead of Δ + 1, the fewer communication rounds are required.