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 …

The chromatic number of a graph G is defined as the minimum number of colors required for
a vertex coloring where no two adjacent vertices are colored the same. The chromatic …

The chromatic number χ (G) χ(G) of a graph GG is a fundamental parameter, whose study
was originally motivated by applications (χ (G) χ(G) is the minimum number of internally …

For the Erdős–Rényi random graph G n, p, we give a precise asymptotic formula for the size
α ˆ t (G n, p) of a largest vertex subset in G n, p that induces a subgraph with average degree …

We consider the t-improper chromatic number of the Erdős–Rényi random graph Gn, p. The t-
improper chromatic number χt (G) is the smallest number of colours needed in a colouring of …

Работа посвящена изучению предельной концентрации значений хроматического
числа случайного гиперграфа H (n, k, p) в биномиальной модели. Доказано, что при …

Erdős and Hajnal conjectured that for every graph H there is a constant such that every
graph G that does not have H as an induced subgraph contains a clique or a stable set of …

Let t be a nonnegative integer and G=(V (G), E (G)) be a graph. For v∈ V (G), let NG (v)={u∈
V (G)\{v}: uv∈ E (G)}. And for S⊆ V (G), we define d S (G; v)=| NG (v)∩ S| for v∈ S and d S …

Asymptotic behaviour of maximum sizes of induced trees and forests has been studied
extensively in last decades, though the overall picture is far from being complete. In this …

Given a graph G, a colouring is an assignment of colours to the vertices of G so that no two
adjacent vertices are coloured the same. If all colour classes have size at most t, then we call …