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 …

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 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 investigate the phase transition in vertex coloring on random graphs, using the extremal
optimization heuristic. Three-coloring is among the hardest combinatorial optimization …

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 analytically describe the typical solution time needed by a backtracking algorithm to
solve the vertex-cover problem on finite-connectivity random graphs. We find two different …

We analyze a minimal model of a growing network. At each time step, a new vertex is added;
then, with probability δ, two vertices are chosen uniformly at random and joined by an …

We analyze graphs in which each vertex is assigned random coordinates in a geometric
space of arbitrary dimensionality and only edges between adjacent points are present. The …

We study both numerically and analytically what happens to a random graph of average
connectivity α when its leaves and their neighbors are removed iteratively up to the point …