How many colors to color a random graph? Cavity, Complexity, Stability and all that
Abstract
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 cq=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.
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