For many random constraint satisfaction problems such as random satisfiability or random
graph or hypergraph coloring, the best current estimates of the threshold for the existence of …

Many NP-complete constraint satisfaction problems appear to undergo a “phase transition”
from solubility to insolubility when the constraint density passes through a critical threshold …

Random instances of constraint satisfaction problems (CSPs) appear to be hard for all
known algorithms when the number of constraints per variable lies in a certain interval …

For a number of random constraint satisfaction problems, such as random k-SAT and
random graph/hypergraph coloring, there are very good estimates of the largest constraint …

Random k-SAT is the single most intensely studied example of a random constraint
satisfaction problem. But despite substantial progress over the past decade, the threshold for …

Survey Propagation is an algorithm designed for solving typical instances of random
constraint satisfiability problems. It has been successfully tested on random 3-SAT and …

For a large number of random constraint satisfaction problems, such as random k-SAT and
random graph and hypergraph coloring, there exist very good estimates of the largest …

The smallest number of edges forming an n‐uniform hypergraph which is not r‐colorable is
denoted by m (n, r). Erdős and Lovász conjectured that. The best known lower bound was …

A 2-coloring of a hypergraph is a mapping from its vertices to a set of two colors such that no
edge is monochromatic. Let H k (n, m) be a random k-uniform hypergraph on n vertices …

For many random constraint satisfaction problems, by now there exist asymptotically tight
estimates of the largest constraint density for which solutions exist. At the same time, for …