Shannon Ogden

collaborators

3 papers

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.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 note on inverting the dijoin of oriented graphs

Universality for transversal powers of Hamilton cycles

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

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