Combinatorics seminar 9th October

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.

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