Let $T$ be a tournament on $X_n=\lbrace 1,2, \ldots ,n \rbrace$ (i.e. an asymmetric relation
$<_T$ on $X_n$). Erdos's famous $S_k$ property says that for any
$k$ elements $i_1 My question, then, is : for any $k$ does there exist $n>k$ and a finite tournament on $X_n$
that has property $S'_k$ ? An obvious necessary condition is that
$n \equiv k ({\rm mod} \ 2^k)$.
Regularity property of tournaments
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probability
combinatorics