Natalie C. Behague

activity

20182026

most citedThe rainbow saturation number is linear

4 citations · 8 across the 18 of their papers we have counts for

collaborators

Showing 2023Show all

5 papers · 1 filter

math.CO2023

An Approximate Counting Version of the Multidimensional Szemerédi Theorem

Natalie Behague, Joseph Hyde, Natasha Morrison +2

For any fixed $d \geq 1$ and subset $X$ of $N^{d}$ , let $r_{X} (n)$ be the maximum cardinality of a subset $A$ of ${1, \dots, n}^{d}$ which does not contain a subset of the form $\…

math.CO2023

A collection of open problems in celebration of Imre Leader's 60th birthday

Rahil Baber, Natalie Behague, Asier Calbet +10

One of the great pleasures of working with Imre Leader is to experience his infectious delight on encountering a compelling combinatorial problem. This collection of open problems…

math.CO2023

Off-Diagonal Commonality of Graphs via Entropy

Natalie Behague, Natasha Morrison, Jonathan A. Noel

A graph $H$ is common if the limit as $n \to \infty$ of the minimum density of monochromatic labelled copies of $H$ in an edge colouring of $K_{n}$ with red and blue is attained by a s…

math.CO2023

Sidorenko-Type Inequalities for Pairs of Trees

Natalie Behague, Gabriel Crudele, Jonathan A. Noel +1

Given two non-empty graphs $H$ and $T$ , write $H ≽ T$ to mean that $t (H, G)^{∣ E (T) ∣} \geq t (T, G)^{∣ E (H) ∣}$ for every graph $G$ , where $t (\cdot, \cdot)$ is the homomorphism d…

math.CO2023

Improved bounds for cross-Sperner systems

Natalie Behague, Akina Kuperus, Natasha Morrison +1

A collection of families $(F_{1}, F_{2}, \dots, F_{k}) \in P ([n])^{k}$ is cross-Sperner if there is no pair $i \neq = j$ for which some $F_i…