This week, Amelia Taylor will speak on “Arbitrary orientations of Hamilton cycles in digraphs” (see abstract below).
The Combinatorics seminar will be on Thursday 9th October at 2pm in R17/18.
Arbitrary orientations of Hamilton cycles in digraphs
Let n be sufficiently large and suppose that G is a digraph on n vertices where every vertex has in- and outdegree at least n/2. We show that G contains every orientation of a Hamilton cycle except, possibly, the antidirected one. The antidirected case was settled by DeBiasio and Molla, where the threshold is n/2+1. Our result is best possible and improves on an approximate result by Haggkvist and Thomason. This is joint work with Louis DeBiasio, Daniela Kühn, Theodore Molla and Deryk Osthus.