1
$\begingroup$

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 $n \equiv k ({\rm mod} \ 2^k)$.

0 Answers 0