The hard-core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics, a multicast model of calls in communication networks, and as a weighted independent set problem in combinatorics, probability and theoretical computer...

Erdös Magic proves the existence of an object but where is it? When the random object has only exponentially small chance of working this is especially challenging. The last years have seen two great successes. Lovász! Moser, followed by Tardos and others, have given an amazingly simple...