# Noon lecture

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On 28.6.2007 at 12:20 in S5, there is the following noon lecture:

# The Bermond-Thomassen conjecture

## Jean-Sébastien Sereni

## Abstract

In 1981, Bermond and Thomassen conjectured that every digraph of minimum out-degree at least 2k-1 contains k vertex-disjoint directed cycles. This conjecture is a simple observation if k is 1, and was proved by Thomassen when k is 2 in 1983. I will survey the (few) results known about the conjecture, and sketch a proof that it holds when k is three. To this end, I will first show that Thomassen's result can be improved. This is joint work with Nicolas Lichiardopol and Attila Por.

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