Natasha Morrison

activity

20242026

collaborators

5 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

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

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.CO2025

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.CO2024

Using polynomials to find lower bounds for $r$ -bond bootstrap percolation

Natasha Morrison, Shannon Ogden

The $r$ -bond bootstrap percolation process on a graph $G$ begins with a set $S$ of infected edges of $G$ (all other edges are healthy). At each step, a healthy edge becomes infecte…

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

A note on inverting the dijoin of oriented graphs

Universality for transversal powers of Hamilton cycles

Thresholds for constrained Ramsey and anti-Ramsey problems

Using polynomials to find lower bounds for r-bond bootstrap percolation

Using polynomials to find lower bounds for $r$ -bond bootstrap percolation