Show that transitive tournaments are worst-case instances for query complexity

Prove that, among all tournaments on n vertices, the worst-case number of k-wise oracle queries needed by the BlitzRank algorithm (Algorithm 1) to identify the top-m items is achieved when the underlying tournament is transitive, thereby extending the transitive-case query complexity bounds to general tournaments.

Background

The paper argues that cycles collapse into strongly connected components, causing multiple vertices to finalize simultaneously and thus intuitively making instances easier than the transitive case.

Formalizing this intuition would justify applying transitive-case bounds as worst-case guarantees for general tournaments.