3 papers
math.CO2022
High-order bootstrap percolation in hypergraphs
Oliver Cooley, Julian Zalla
Motivated by the bootstrap percolation process for graphs, we define a new, high-order generalisation to -uniform hypergraphs, in which we infect -sets of vertices for some i…
math.CO2021
Loose cores and cycles in random hypergraphs
Oliver Cooley, Mihyun Kang, Julian Zalla
Inspired by the study of loose cycles in hypergraphs, we define the \emph{loose core} in hypergraphs as a structure which mirrors the close relationship between cycles and -core…
math.CO2020
Longest paths in random hypergraphs
Oliver Cooley, Frederik Garbe, Eng Keat Hng +3
Given integers with , we consider the length of the longest -tight path in the binomial random -uniform hypergraph . We show that this length…