A well-known conjecture in computer science and statistical physics is that Glauber
dynamics on the set of k-colorings of a graph G on n vertices with maximum degree Δ is …

We present an improved “cooling schedule” for simulated annealing algorithms for
combinatorial counting problems. Under our new schedule the rate of cooling accelerates as …

We show that the natural Glauber dynamics mixes rapidly and generates a random proper
edge-coloring of a graph with maximum degree Δ whenever the number of colors is at least …

We study the hard-core (gas) model defined on independent sets of an input graph where
the independent sets are weighted by a parameter (aka fugacity) λ>0. For constant Δ, the …

We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for
computing the partition function of a two-state spin system on an arbitrary graph, when the …

We present a randomized algorithm that takes as input an undirected n-vertex graph G with
maximum degree Δ and an integer k> 3Δ, and returns a random proper k-coloring of G. The …

We study a simple Markov chain, known as the Glauber dynamics, for generating a random
k‐coloring of an n‐vertex graph with maximum degree Δ. We prove that, for every ε> 0, the …

It is well known that the spectral radius of a tree whose maximum degree is Δ cannot exceed
2Δ− 1. In this paper we derive similar bounds for arbitrary planar graphs and for graphs of …

We present improved bounds for randomly sampling $ k $-colorings of graphs with
maximum degree $\Delta $; our results hold without any further assumptions on the graph …

We introduce efficient algorithms for approximate sampling from symmetric Gibbs
distributions on the sparse random (hyper) graph. The examples we consider include (but …