Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical
computer science will welcome the new edition of this book.”-MAA Reviews Maintaining a …

We develop a notion of containment for independent sets in hypergraphs. For every r r-
uniform hypergraph GG, we find a relatively small collection\mathcal CC of vertex subsets …

For integers s,t≥2, the Ramsey number r(s,t) denotes the minimum n such that every n-
vertex graph contains a clique of order s or an independent set of order t. In this paper we …

For two graphs T and H with no isolated vertices and for an integer n, let ex (n, T, H) denote
the maximum possible number of copies of T in an H-free graph on n vertices. The study of …

We develop a new technique that allows us to show in a unified way that many well-known
combinatorial theorems, including Turan's theorem, Szemerédi's theorem and Ramsey's …

Extremal problems in hypergraph colouring originate implicitly from Hilbert's theorem on
monochromatic affine cubes (1892) and van der Waerden's theorem on monochromatic …

Extremal Finite Set Theory surveys old and new results in the area of extremal set system
theory. It presents an overview of the main techniques and tools (shifting, the cycle method …

The Ramsey number Rk;/, introduced by Ramsey [16] in relation to logic, is the smallest
positive integer n such that every graph on n vertices contains a subgraph isomorphic to Kk …

The graph removal lemma states that any graph on n vertices with o (nh) copies of a fixed
graph H on h vertices may be made H-free by removing o (n2) edges. Despite its innocent …

In this survey we describe a recently-developed technique for bounding the number (and
controlling the typical structure) of finite objects with forbidden substructures. This technique …