Abstract: Let Γ ,n   denote all m  × n strongly connected bipartite tournaments and α（ m ,n）the maxi- mal integer k such that every m  × n bipartite tournament contains at least a k  × k transitive bipartite subtournament．Let t（ m ,n ,k ,l）＝ max｛t（ T _{m ,n}  ,k ,l）：T _{m ,n}   ∈ Γ ,n ｝,where t（ T _{m ,n}  ,k ,l）is the
number of k× l（ k ≥2,l ≥2）transitive bipartite subtournaments contained in T _{m ,n}   ∈ Γ ,n ．We ob-
tain a method of graph theory for solving some integral programmings,investigate the upper bounds of α（ m ,n）and obtain t（ m ,n ,k ,l）.

Key words: reverse arc, transitive, bipartite tournament, enumeration