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

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 …

A concise, comprehensive introduction to the topic of statistical physics of combinatorial
optimization, bringing together theoretical concepts and algorithms from computer science …

Methods of statistical mechanics are applied to two important NP-complete combinatorial
optimization problems. The first is the chromatic number problem, which seeks the minimal …

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 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 …

Recently, it has been recognized that phase transitions play an important role in the
probabilistic analysis of combinatorial optimization problems. However, there are in fact …

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 q‐state ferromagnetic Potts model on the n‐vertex complete graph known as
the mean‐field (Curie‐Weiss) model. We analyze the Swendsen‐Wang algorithm which is a …