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

Details How many colors to color a random graph? Cavity, Complexity, Stability and all that How many colors to color a random graph? Cavity, Complexity, Stability and all that

2004-09-17

arxiv.org/abs/cond-mat/0409448v2

Progress of Theoretical Physics Supplement No.157 (2005) pp. 357-360

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures, proceeding of "Statistical Physics of Disordered Systems and Its Applications", Hayama (Japan), July 2004

Scientific paper

10.1143/PTPS.157.357

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.

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