Richard Mycroft

collaborators

3 papers

math.CO2018

Classification of maximum hittings by large families

Candida Bowtell, Richard Mycroft

For integers $r$ and $n$ , where $n$ is sufficiently large, and for every set $X \subseteq [n]$ we determine the maximal left-compressed intersecting families $\mathcal{A}\subseteq…

math.CO2018

Hamilton $ℓ$ -cycles in randomly-perturbed hypergraphs

Andrew McDowell, Richard Mycroft

We prove that for integers $2 \leq ℓ < k$ and a small constant $c$ , if a $k$ -uniform hypergraph with linear minimum codegree is randomly `perturbed' by changing non-edges to edg…

math.CO2016

The minimum vertex degree for an almost-spanning tight cycle in a $3$ -uniform hypergraph

Oliver Cooley, Richard Mycroft

We prove that any $3$ -uniform hypergraph whose minimum vertex degree is at least $(\frac{5}{9} + o (1)) (2 n)$ admits an almost-spanning tight cycle, that is, a ti…

Classification of maximum hittings by large families

Hamilton ℓ-cycles in randomly-perturbed hypergraphs

The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph

Hamilton $ℓ$ -cycles in randomly-perturbed hypergraphs

The minimum vertex degree for an almost-spanning tight cycle in a $3$ -uniform hypergraph