Abstract
Let G be a subgraph of a complete bipartite graph Kn,n. Let N(G) be a 0-1 incidence matrix with edges of Kn,n against images of G under the automorphism group of Kn,n. A diagonal form of N(G) is found for every G, and the question as to whether the row space of N(G) over Zp contains the vector of all 1's is settled. This implies a new proof of Caro and Yuster's results on zero-sum bipartite Ramsey numbers, and provides necessary and sufficient conditions for the existence of a signed bipartite graph design.
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