A Partial Order on Bipartite Graphs with n Vertices

The paper examines a partial order on bipartite graphs (X1, X2, E) with n vertices, X1∪X2={1,2,…,n}. The basis of such bipartite graph is X1 = {1,2,…,k}, 0≤k≤n. If U = (X1, X2, E(U)) and V = (Y1,Y2, E(V)) then U≤V iff |X1| ≤ |Y1| and {(i,j) E(U): j>|Y1|} = ={(i,j) E(V):i≤|X1|}. This partial order is a natural partial order of subobjects of an object in a triangular category with bipartite graphs as morphisms.