81 citations · 322 across the 17 of their papers we have counts for
6 papers · 1 filter
Contagious sets in a degree-proportional bootstrap percolation process
Frederik Garbe, Andrew McDowell, Richard Mycroft
We study the following bootstrap percolation process: given a connected graph , a constant and an initial set of \emph{infected} vertices, at ea…
Unavoidable trees in tournaments
Richard Mycroft, Tássio Naia
An oriented tree on vertices is unavoidable if every tournament on vertices contains a copy of . In this paper we give a sufficient condition for to be unavoidab…
Hamilton cycles in hypergraphs below the Dirac threshold
Frederik Garbe, Richard Mycroft
We establish a precise characterisation of -uniform hypergraphs with minimum codegree close to which contain a Hamilton -cycle. As an immediate corollary we identify th…
Triangle-tilings in graphs without large independent sets
József Balogh, Andrew McDowell, Theodore Molla +1
We study the minimum degree necessary to guarantee the existence of perfect and almost-perfect triangle-tilings in an -vertex graph with sublinear independence number. In th…
The minimum vertex degree for an almost-spanning tight cycle in a -uniform hypergraph
Oliver Cooley, Richard Mycroft
We prove that any -uniform hypergraph whose minimum vertex degree is at least admits an almost-spanning tight cycle, that is, a ti…
An asymptotic multipartite Kühn-Osthus theorem
Ryan R. Martin, Richard Mycroft, Jozef Skokan
In this paper we prove an asymptotic multipartite version of a well-known theorem of Kühn and Osthus by establishing, for any graph with chromatic number , the asymptotic mu…