| Abstract： |
An n-rournament T is called k-strong($1\leq k \leq n-2$),if every $(n+1-k)\rightarrow$ subtournament of T is strongly connected.This paper proves that a score vector $(s_1,s_2,\cdots,s_n)$,where $s_1\leq s_2\leq \cdots \leq s_n$,is the score vector of some k-strong tournament if and only if $min{t_1,t_2,\cdots,t_{n-1}}\geq k$,where $t_j=s_1+s_2+\cdots +s_j-j(j-1)/2,j=1,2,\cdots ,n-1$. |
