Joseph Hyde

activity

20232026

collaborators

6 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.CO2025

Universality for transversal powers of Hamilton cycles

Emily Heath, Joseph Hyde, Natasha Morrison +1

Let $k \geq 2$ and let $G = {G_{1}, \dots, G_{m}}$ be a collection of graphs on a common vertex set of cardinality $n$ . We show that if each graph in $G$ has minimum degree…

math.CO2024

Thresholds for constrained Ramsey and anti-Ramsey problems

Natalie Behague, Robert Hancock, Joseph Hyde +2

Let $H_{1}$ and $H_{2}$ be graphs. A graph $G$ has the constrained Ramsey property for $(H_{1}, H_{2})$ if every edge-colouring of $G$ contains either a monochromatic copy of $H_{1}$ or a rai…

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

Spanning trees in pseudorandom graphs via sorting networks

Joseph Hyde, Natasha Morrison, Alp Müyesser +1

We show that $(n, d, λ)$ -graphs with $λ = O (d / lo g^{3} n)$ are universal with respect to all bounded degree spanning trees. This significantly improves upon the previous best bound due t…

math.CO2023

Turán Colourings in Off-Diagonal Ramsey Multiplicity

Joseph Hyde, Jae-baek Lee, Jonathan A. Noel

The \emph{Ramsey multiplicity constant} of a graph $H$ is the limit as $n$ tends to infinity of the minimum density of monochromatic labeled copies of $H$ in a $2$ -edge colouring o…