Given graphs $ G_1,\ldots, G_s $ all on the same vertex set and a graph $ H $ with $ e
(H)\leq s $, a copy of $ H $ is transversal or rainbow if it contains at most one edge from each …

Let $ P:\F\times\F\to\F $ be a polynomial of bounded degree over a finite field $\F $ of large
characteristic. In this paper we establish the following dichotomy: either $ P $ is a moderate …

A graph G is called quasirandom if it possesses typical properties of the corresponding
random graph G (n, p) with the same edge density as G. A well-known theorem of Chung …

The classical hypergraph Ramsey number rk (s, n) is the minimum N such that for every red-
blue coloring of the k-tuples of {1,…, N}, there are s integers such that every k-tuple among …

We examine the correspondence between the various notions of quasirandomness for k‐
uniform hypergraphs and σ‐algebras related to measurable hypergraphs. This gives a …

Given k⩾ 2 k\geqslant2 and two kk‐graphs (kk‐uniform hypergraphs) FF and HH, an FF‐
factor in HH is a set of vertex‐disjoint copies of FF that together cover the vertex set of H H …

Let-uniform hypergraph can have. Our work connects previous notions on linear hypergraph
quasirandomness by Kohayakawa, Rödl, and Skokan, and by Conlon, Hàn, Person, and …

We develop a theory of high-arity PAC learning, which is statistical learning in the presence
of" structured correlation". In this theory, hypotheses are either graphs, hypergraphs or, more …

Given s⩾ k⩾ 3, let h (k)(s) be the minimum t such that there exist arbitrarily large k‐uniform
hypergraphs H whose independence number is at most polylogarithmic in the number of …

Over the past several years, numerous authors have explored model theoretically motivated
combinatorial conditions that ensure that a graph has an efficient regular decomposition in …