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 k⩾ 3 be a fixed integer and let Zk (G) be the number of k-colourings of the graph G. For
certain values of the average degree, the random variable Zk (G (n, m)) is known to be …

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 k be a fixed integer and fk (n, p) denote the probability that the random graph G (n, p) is k‐
colorable. We show that for k≥ 3, there exists dk (n) such that for any ϵ> 0, n → ∞ f_k\biggl …

Let $ G (n, m) $ be the random graph on $ n $ vertices with $ m $ edges. Let $ d= 2m/n $ be
its average degree. We prove that $ G (n, m) $ fails to be $ k $-colorable with high probability …

In this paper we study acyclic colouring in the random subgraph $\mathit {G} $ of the
complete graph $\mathit {K} _n $ on $\mathit {n} $ vertices where each edge is present with …

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 …

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 …

A random geometric graph G_n is obtained as follows. We take X_1,X_2,...,X_n∈R^d at
random (iid according to some probability distribution ν on R^d). For i≠j we join X_i and X_j …

Let Cnk be the kth power of a cycle on n vertices (ie the vertices of Cnk are those of the n-
cycle, and two vertices are connected by an edge if their distance along the cycle is at most …