A New Perspective on Dirac-Type Results in Hypergraphs
Professor of Mathematics
Richard Mycroft presents an asymptotically optimal minimum positive codegree condition for Hamilton cycles in k-graphs, generalizing Dirac's theorem for hypergraphs.
Abstract: I will present an asymptotically best-possible minimum positive codegree condition for the existence of a Hamilton \ell-cycle in a k-graph. This gives a natural generalisation for hypergraphs of Dirac's celebrated theorem on Hamilton cycles in graphs of high minimum degree. Most previous results of this nature have instead considered minimum codegree or minimum \ell-degree conditions. I will argue for the advantages of minimum positive codegree conditions over minimum codegree conditions, and suggest further possible directions for study with this perspective. This is joint work with Camila Zárate-Guerén.
This lecture was part of the LMS Computer Science Colloquium 2025, which took place at De Morgan House, London on Tuesday 9 December 2025 and online via Zoom.