An n-vertex graph is called C-Ramsey if it has no clique or independent set of size (ie, if it
has near-optimal Ramsey behavior). In this paper, we study edge statistics in Ramsey …

Consider integers k, ℓ such that 0⩽ ℓ⩽ k 2. Given a large graph G, what is the fraction of k‐
vertex subsets of G which span exactly ℓ edges? When G is empty or complete, and ℓ is zero …

An $ n $-vertex graph is called $ C $-Ramsey if it has no clique or independent set of size $
C\log n $. All known constructions of Ramsey graphs involve randomness in an essential …

Consider a quadratic polynomial $ f\left (\xi_ {1},\dots,\xi_ {n}\right) $ of independent
Bernoulli random variables. What can be said about the concentration of $ f $ on any single …

An n-vertex graph is called C-Ramsey if it has no clique or independent set of size. All
known constructions of Ramsey graphs involve randomness in an essential way, and there …

One of the central goals in extremal combinatorics is to understand how the global structure
of a combinatorial object, eg a graph, hypergraph or set system, is affected by local …

We call a pair $(m, f) $ of integers, $ m\geq 1$, $0\leq f\leq\binom {m}{2} $,\emph {absolutely
avoidable} if there is $ n_0 $ such that for any pair of integers $(n, e) $ with $ n> n_0 $ and …

An important theme of recent research in Ramsey theory has been establishing
pseudorandomness properties of Ramsey graphs. An $ N $-vertex graph is called $ C …

Given an $ n $-vertex graph $ G $, let $\hom (G) $ denote the size of a largest homogeneous
set in $ G $ and let $ f (G) $ denote the maximal number of distinct degrees appearing in an …

In this paper we investigate the extremal relationship between two well-studied graph
parameters: the order of the largest homogeneous set in a graph G and the maximal number …