We consider the problem of coloring the vertices of a large sparse random graph with a
given number of colors so that no adjacent vertices have the same color. Using the cavity …

We study the graph coloring problem over random graphs of finite average connectivity c.
Given a number q of available colors, we find that graphs with low connectivity admit almost …

We study the graph coloring problem over random graphs of finite average connectivity c.
Given a number q of available colors, we find that graphs with low connectivity admit almost …

Based on a non-rigorous formalism called the “cavity method”, physicists have put forward
intriguing predictions on phase transitions in diluted mean-field models, in which the …

We consider the problem of coloring Erdös-Rényi and regular random graphs of finite
connectivity using q colors. It has been studied so far using the cavity approach within the so …

We study constraint satisfaction problems on the so-called planted random ensemble. We
show that for a certain class of problems, eg, graph coloring, many of the properties of the …

Finding the mean of the total number N tot of stationary points for N-dimensional random
energy landscapes is reduced to averaging the absolute value of the characteristic …

The set of solutions of random constraint satisfaction problems (zero energy groundstates of
mean-field diluted spin glasses) undergoes several structural phase transitions as the …

We offer a solution to a long-standing problem in the theory of networks, the creation of a
plausible, solvable model of a network that displays clustering or transitivity—the propensity …

We exploit a relation between the mean number N m of minima of random Gaussian
surfaces and extreme eigenvalues of random matrices to understand the critical behavior of …