Randomness and Regularity à la Szemerédi Ross

  title={Randomness and Regularity {\`a} la Szemer{\'e}di Ross},
  author={Matt Richardson},
In this talk we discuss the influence of probabilistic reasoning in combinatorics and related fields. In particular, we discuss the use of Szemerédi’s Regularity Lemma as a quantitative method of applying probabilistic arguments to deterministic graphs. Recall that a graph G = (V, E) consists of a vertex set V and a set of edges E ⊆ {{u, v} | u, v ∈ V }. We shall denote by Kn a graph on n vertices where every two vertices are adjacent. We will often write e(G) := |E|. 1 Motivating Questions Let… CONTINUE READING