A recurrence for bounds on dominating sets in \(k\)-majority tournaments (Q640421)

The paper establishes new upper bounds for the size of a smallest dominating set in \(k\)-majority tournaments that considerably improve upon previous bounds for small \(k\), where a \(k\)-majority tournament is realized by \(2k - 1\) linear orders on the set of vertices in which a vertex \(u\) dominates \(v\) if \(u\) precedes \(v\) in at least k of the orders. In particular, it is shown that 3-majority tournaments are dominated by at most 12 vertices.