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 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 in this paper the structure of solutions in the random hypergraph coloring problem
and the phase transitions they undergo when the density of constraints is varied …

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 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 …

Let k⩾ 3 be a fixed integer. We exactly determine the asymptotic distribution of ln Zk (G (n,
m)), where Zk (G (n, m)) is the number of k-colourings of the random graph G (n, m). A crucial …

The problem of vertex coloring in random graphs is studied using methods of statistical
physics and probability. Our analytical results are compared to those obtained by exact …

We study the problem of bicolouring random hypergraphs, both numerically and analytically.
We apply the zero-temperature cavity method to find analytical results for the phase …

We review the understanding of the random constraint satisfaction problems, focusing on the
q-coloring of large random graphs, that has been achieved using the cavity method. We also …