Two teams A and B can be
compared by matching each player in A against each player in B. We say that A > B
if and only if the players of A collectively win more games against players of B than
they lose. If there are n teams T1,T2,⋯,Tn, then the outcomes of the matches
between the various teams may be represented by an oriented graph Hn on n nodes
in which an arc goes from the i-th node to the j-th node if and only if Tj> Tj. It is
shown that any oriented graph can be generated in this way, and that the minimum
number of players necessary to generate any oriented graph Hn is of the order of
nz∕logn.
