We review recent progress on the statiscal physics study of the problem of
coloring random graphs with q colors. We discuss the existence of a threeshold
at connectivity c_q=2q log q-log q-1+o(1) separting two phases which are
respectivily COL(orable) and UNCOL(orable) with q colors; We also argue that
the so-called one-step replica symmetry breaking ansatz used to derive these
results give it exact threshold values, and draw a general phase diagram of the
problem.Comment: 4 pages, 2 figures, proceeding of "Statistical Physics of Disordered
Systems and Its Applications", Hayama (Japan), July 200