Finding a reasonably good upper bound for the clique number of Paley graphs is an open
problem in additive combinatorics. A recent breakthrough by Hanson and Petridis using …

Let $ GP (q, d) $ be the $ d $-Paley graph defined on the finite field $\mathbb {F} _q $. It is
notoriously difficult to improve the trivial upper bound $\sqrt {q} $ on the clique number of …

We describe a new class of maximal cliques, with a vector space structure, of Cayley graphs
defined on the additive group of a field. In particular, we show that in the cubic Paley graph …

We initiate the systematic study of the following Tur\'an-type question. Suppose $\Gamma $
is a graph with $ n $ vertices such that the edge density between any pair of subsets of …

Motivated by the well-known Paley graphs over finite fields and their generalizations, in this
paper we explore a natural multiplicative-additive analogue of such graphs arising from …

Sárközy's theorem states that dense sets of integers must contain two elements whose
difference is ak th power. Following the polynomial method breakthrough of Croot, Lev and …