University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > Trees in Tournaments

## Trees in TournamentsAdd to your list(s) Download to your calendar using vCal - Alistair Benford (Birmingham)
- Thursday 25 February 2021, 16:00-17:00
- https://bham-ac-uk.zoom.us/j/86238837160.
If you have a question about this talk, please contact M.Jenssen. Given an n-vertex oriented tree T, what is the smallest size a tournament G must be, in order to guarantee G contains a copy of T? A strengthening of Sumner’s conjecture poses that it is enough for G to have (n+k-1) vertices, where k is the number of leaves of T. Recently, Dross and Havet used a method of median orders to prove that this is true for arborescences—i.e. trees with edges oriented outwards from a specified root vertex. We show that median orders can make further progress towards (n+k-1), by proving that there exists a constant C such that |G|=(n+Ck) is enough, as well as confirming a separate conjecture that |G|=(n+k-2) is enough, provided we allow n to grow large with k fixed. In this talk we shall discuss these results and further progress that could be made. Joint work with Richard Montgomery This talk is part of the Combinatorics and Probability Seminar series. ## This talk is included in these lists:- https://bham-ac-uk.zoom.us/j/86238837160
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