What is Road coloring theorem?

In graph theory the road coloring theorem, known previously as the road coloring conjecture, deals with synchronized instructions. The issue involves whether by using such instructions, one can reach or locate an object or destination from any other point within a network. In the real world, this phenomenon would be as if you called a friend to ask for directions to his house, and he gave you a set of directions that worked no matter where you started from. This theorem also has implications in symbolic dynamics.

The theorem was first conjectured by Roy Adler and Benjamin Weiss. It was proved by Avraham Trahtman.