David Conlon

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4 papers · 1 filter

math.CO2024

On the clique number of random Cayley graphs and related topics

David Conlon, Jacob Fox, Huy Tuan Pham +1

We prove that a random Cayley graph on a group of order $N$ has clique number $O (lo g N lo g lo g N)$ with high probability. This bound is best possible up to the constant factor f…

math.CO2024

Big line or big convex polygon

David Conlon, Jacob Fox, Xiaoyu He +3

Let $E S_{ℓ} (n)$ be the minimum $N$ such that every $N$ -element point set in the plane contains either $ℓ$ collinear members or $n$ points in convex position. We prove that th…

math.CO2023

Homogeneous structures in subset sums and non-averaging sets

David Conlon, Jacob Fox, Huy Tuan Pham

We show that for every positive integer $k$ there are positive constants $C$ and $c$ such that if $A$ is a subset of ${1, 2, \dots, n}$ of size at least $C n^{1/ k}$ , then, for so…

math.CO2023

Simplicial Turán problems

David Conlon, Simón Piga, Bjarne Schülke

A simplicial complex $H$ consists of a pair of sets $(V, E)$ where $V$ is a set of vertices and $E \subseteq P (V)$ is a collection of subsets of $V$ closed under taking subs…