10 papers · 1 filter
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 -graph to contain a colour-biased tight Hamilton cycle. This confirms a conj…
Universality for transversal powers of Hamilton cycles
Emily Heath, Joseph Hyde, Natasha Morrison +1
Let and let be a collection of graphs on a common vertex set of cardinality . We show that if each graph in has minimum degree…
Using polynomials to find lower bounds for -bond bootstrap percolation
Natasha Morrison, Shannon Ogden
The -bond bootstrap percolation process on a graph begins with a set of infected edges of (all other edges are healthy). At each step, a healthy edge becomes infecte…
Generalized Ramsey numbers via conflict-free hypergraph matchings
Andrew Lane, Natasha Morrison
Given graphs and an integer , the generalized Ramsey number, denoted , is the minimum number of colours needed to edge-colour such that every copy of…
Layered subgraphs of the hypercube
Natalie Behague, Imre Leader, Natasha Morrison +1
A subgraph of the -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…
A note on inverting the dijoin of oriented graphs
Natalie Behague, Tom Johnston, Natasha Morrison +1
For an oriented graph and a set , the inversion of in is the graph obtained from by reversing the orientation of each edge that has both endpoints…