Monday October 6th at 4.30pm

A tournament is an orientation of the arcs of a complete undirected graph. In this talk, median orders are used to prove results

about the two following conjectures. The first one due to Seymour asserts that every digraph contains a vertex

whose second outneighborhood larger or equal to its (first) outneighborhood. The second one due to Sumner states that a tournament

of order

Sumner's for arborescences. We also prove that a tournament of order