Let G= G (n, m) be a random graph whose average degree d= 2 m/n is below the k-
colorability threshold. If we sample ak-coloring σ of G uniformly at random, what can we say …

Let $ G= G (n, m) $ be a random graph whose average degree $ d= 2m/n $ is below the $ k
$-colorability threshold. If we sample a $ k $-coloring $\sigma $ of $ G $ uniformly at random …

Let k⩾ 3 be a fixed integer. We exactly determine the asymptotic distribution of ln Zk (G (n,
m)), where Zk (G (n, m)) is the number of k-colourings of the random graph G (n, m). A crucial …

Let 0< p< 1 be fixed. Shamir and Spencer proved in the 1980s that the chromatic number of
a random graph in G (n, p) is concentrated in an interval of length about n^{1/2}. In this …

Let $\Omega_q $ denote the set of proper $ q $-colorings of the random graph $ G_ {n, m},
m= dn/2$ and let $ H_q $ be the graph with vertex set $\Omega_q $ and an edge …

Shamir and Spencer proved in the 1980s that the chromatic number of the binomial random
graph G (n, p) is concentrated in an interval of length at most\omega\sqrt {n}, and in the …

We consider the problem of sampling a proper $ k $-coloring of a graph of maximal degree
$\Delta $ uniformly at random. We describe a new Markov chain for sampling colorings, and …

Abstract Let T (H, G n) be the number of monochromatic copies of a fixed connected graph H
in a uniformly random coloring of the vertices of the graph G n. In this paper we give a …

Our goal is to color the edges of a random graph Gn, m (a graph drawn uniformly at random
from all graphs on n vertices with exactly m edges) with a fixed number r of colors such that …

In this work we show that with high probability the chromatic number of a graph sampled
from the random regular graph model Gn, d for d= o (n1/5) is concentrated in two …