Pseudo-telepathy, entanglement, and graph colorings

Quantum entanglement allows for a phenomenon called pseudo-telepathy. This can be used to devise a simple experiment demonstrating the existence of quantum entanglement, provided that the parameters are chosen such that it is impossible to win the game without entanglement or communication (or telepathy). We describe a close connection between pseudo-telepathy and graph coloring and use this to correct previous beliefs on the possibility of doing pseudo-telepathy.