Optimal seeding in balanced knockout tournaments has only been studied in very limited settings, for example, maximizing predictive power for up to 8 players using only the relative ranking of the players (ordinal information). We broaden the scope of the analysis along several dimensions: tournaments of size up to 128, different player models, ordinal as well as cardinal solutions, and two add...

In this paper, we study the density of fixed strongly connected subtournaments on 5 vertices in large tournaments. We determine the maximum density asymptotically for three tournaments as well as extremal families for each tournament. We use Razborov’s semidefinite method for flag algebras to prove the upper bounds.

Let T be a ,nite set of ,nite tournaments and HT the countable homogeneous directed graph which does not embed any of the tournaments in T. We will completely describe the vertex partition property HT. c © 2002 Elsevier Science B.V. All rights reserved.