7 papers
Trees and treelike structures in dense digraphs
Richard Mycroft, Tássio Naia
We prove that every oriented tree on vertices with bounded maximum degree appears as a spanning subdigraph of every directed graph on vertices with minimum semidegree at le…
Towards Pósa's Conjecture for -graphs
Debmalya Bandyopadhyay, Allan Lo, Richard Mycroft
We prove that every -graph on vertices with minimum codegree contains the square of a tight Hamilton cycle. This strengthens a theorem of Bede…
Two new results on maximal left-compressed intersecting families
Allan Flower, Richard Mycroft
This paper presents two new results on the theory of maximal left-compressed intersecting families (MLCIFs). First, we answer a question raised by Barber by showing that the number…
Positive codegree thresholds for perfect matchings in hypergraphs
Richard Mycroft, Camila Zárate-Guerén
We give, for each , the precise best possible minimum positive codegree condition for a perfect matching in a large -uniform hypergraph on vertices. Specifical…
Positive codegree thresholds for Hamilton cycles in hypergraphs
Richard Mycroft, Camila Zárate-Guerén
For each and we give an asymptotically best possible minimum positive codegree condition for the existence of a Hamilton -cycle in a -uni…
Perfect tilings of 3-graphs with the generalised triangle
Candida Bowtell, Amarja Kathapurkar, Natasha Morrison +1
We establish a best-possible minimum codegree condition for the existence of a perfect tiling of a -uniform hypergraph with copies of the generalised triangle , which is…