Hamilton cycles in random hypergraphs

Speaker: 

Catherine Greenhill

Affiliation: 

University of New South Wales

Date: 

Tue, 04/04/2017 -
1:00pm to 2:00pm

Venue: 

RC-4082, The Red Centre, UNSW

Abstract: 

The small subgraph conditioning method was introduced by Robinson and Wormald (1992, 1994) to prove that a random $r$-regular graph contains a Hamilton cycle with probability which tends to 1 as the number of vertices tends to infinity, so long as the degree $r$ is at least 3.  The method involves a careful analysis of variance and has been applied to prove many other structural properties of random regular graphs.  Much less work has been done in the hypergraph setting.

I will discuss recently-completed work on the analysis of the number of Hamilton cycles in random regular uniform hypergraphs.  In particular, we find a constant degree threshold which is sufficient for the existence of a Hamilton cycle with probability which tends to 1, as conjectured by Dudek, Frieze, Rucinski and Sileikis in 2015.

This is joint work with Daniel Altman, Mikhail Isaev and Reshma Ramadurai.

School Seminar Series: