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 …

Accepted Manuscript Page 1 Annika Heckel Non-concentration of the chromatic number of a
random graph Journal of the American Mathematical Society DOI: 10.1090/jams/957 Accepted …

We study the following two problems: i) Given a random graph $ G_ {n, m} $(a graph drawn
uniformly at random from all graphs on $ n $ vertices with exactly $ m $ edges), can we color …

Given an arbitrary graph $ G $ we study the chromatic number of a random subgraph $ G_
{1/2} $ obtained from $ G $ by removing each edge independently with probability $1/2 …

We prove that for every constant δ> 0 the chromatic number of the random graph G (n, p)
with p= n− 1/2− δ is asymptotically almost surely concentrated in two consecutive values …

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 ωn denote a random graph with vertex set {1, 2,…, n}, such that each edge is present
with a prescribed probability p, independently of the presence or absence of any other …

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 …

We consider vertex partitions of the binomial random graph $ G_ {n, p} $. For $ np\to\infty $,
we observe the following phenomenon: in any partition into asymptotically fewer than $\chi …