D. Conlon

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math.CO2026

Combinatorial theorems relative to sparse sets

David Conlon

A key theme in modern extremal combinatorics is the study of classical combinatorial theorems relative to sparse subsets of their natural settings. Here we describe some of the rec…

math.CO2025

Sums of algebraic dilates

David Conlon, Jeck Lim

We show that if $I^»_{1}, \dots, I^»_{k}$ are algebraic numbers, then $∣ A + I^»_{1} \cdot A + \dots + I^»_{k} \cdot A ∣ \geq H (I^»_{1}, \dots, I^»_{k}) ∣ A ∣ - o (∣ A ∣)$ for all finite subsets $A$ of $C$ , w…

math.CO2025

Even cycles in graphs avoiding longer even cycles

David Conlon, Eion Mulrenin, Cosmin Pohoata

A conjecture of VerstraÃ«te states that for any fixed $ℓ < k$ there exists a positive constant $c$ such that any $C_{2 k}$ -free graph $G$ contains a $C_{2 ℓ}$ -free subgraph wit…

math.CO2024

Sums of dilates over groups of prime order

David Conlon, Jeck Lim

For $p$ prime, $A \subseteq Z / p Z$ and $I^» \in Z$ , the sum of dilates $A + I^» \cdot A$ is defined by \[A + Î»\cdot A = \{a + Î»a' : a, a' \in A\}.\] The bas…