Natalie C. Behague

collaborators

10 papers

math.CO2026

A minimum-degree threshold for colour-biased Hamilton cycles in hypergraphs

Natalie Behague, Felix Christian Clemen, Joseph Hyde +1

We determine the asymptotically best possible minimum vertex degree condition forcing a two-coloured $3$ -graph to contain a colour-biased tight Hamilton cycle. This confirms a conj…

math.CO2026

Compatible Hamilton cycles in graphs with large minimum degree

Natalie Behague, Francesco Di Braccio, Bertille Granet +1

The renowned theorem of Dirac states that if $G$ is a graph with minimum degree at least $n /2$ then $G$ has a Hamilton cycle. A natural generalisation asks what properties of an ed…

math.CO2025

A proof of the Kim-Vu sandwich conjecture

Natalie Behague, Daniel Il'koviÄ, Richard Montgomery

In 2004, Kim and Vu conjectured that, when $d = I ¨ (lo g n)$ , the random $d$ -regular graph $G_{d} (n)$ can be sandwiched with high probability between two random binomial graphs $G (n, p)$ …

math.CO2025

Nearly all known Euclidean Ramsey sets are subsoluble

Natalie Behague

A finite set $X$ in a Euclidean space $R^{d}$ is called Ramsey if for every $k$ there exists an integer $n$ such that whenever $R^{n}$ is coloured with $k$ colours, t…

math.CO2025

A note on inverting the dijoin of oriented graphs

Natalie Behague, Tom Johnston, Natasha Morrison +1

For an oriented graph $D$ and a set $X \subseteq V (D)$ , the inversion of $X$ in $D$ is the graph obtained from $D$ by reversing the orientation of each edge that has both endpoints…

math.CO2025

Colour-biased Hamilton cycles in dense graphs and random graphs

Natalie Behague, Debsoumya Chakraborti, Jared LeÃ³n

A classical result of Dirac says that every $n$ -vertex graph with minimum degree at least $\frac{n}{2}$ contains a Hamilton cycle. A `discrepancy' version of Dirac's theorem was sh…