Natasha Morrison

activity

20232026

most citedA note on inverting the dijoin of oriented graphs

1 citations · 1 across the 10 of their papers we have counts for

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.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

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…

math.CO2024

Generalized Ramsey numbers via conflict-free hypergraph matchings

Andrew Lane, Natasha Morrison

Given graphs $G, H$ and an integer $q \geq 2$ , the generalized Ramsey number, denoted $r (G, H, q)$ , is the minimum number of colours needed to edge-colour $G$ such that every copy of…

math.CO2024

Layered subgraphs of the hypercube

Natalie Behague, Imre Leader, Natasha Morrison +1

A subgraph of the $n$ -dimensional hypercube is called 'layered' if it is a subgraph of a layer of some hypercube. In this paper we show that there exist subgraphs of the cube of ar…

math.CO2024★ 1 cited

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.CO2024

On multicolor Turán numbers

József Balogh, Anita Liebenau, Letícia Mattos +1

We address a problem which is a generalization of Turán-type problems recently introduced by Imolay, Karl, Nagy and Váli. Let $F$ be a fixed graph and let $G$ be the union of $k$ e…

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…

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

Universality for transversal powers of Hamilton cycles

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

Generalized Ramsey numbers via conflict-free hypergraph matchings

Layered subgraphs of the hypercube

A note on inverting the dijoin of oriented graphs

On multicolor Turán numbers

Thresholds for constrained Ramsey and anti-Ramsey problems

An Approximate Counting Version of the Multidimensional Szemerédi Theorem

Spanning trees in pseudorandom graphs via sorting networks

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