The Properties of Transitive Bipartite Tournaments
Tan Shang-wang · Shuxue jikan · 2003
Let Γ~* (m,n) denote all m×n strongly connected bipartite tournaments and α(m,n) the maximal 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~* (m,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~* (m,n). We obtain 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).