Geodesic
On imbalances in oriented bipartite graphs
Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 136-141.

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An oriented bipartite graph is the result of assigning a direction to each edge of a simple bipartite graph. For any vertex $x$ in an oriented bipartite graph $D(U,V)$, let $d_{x}^{+}$ and $d_{x}^{-}$ respectively denote the outdegree and indegree of $x$. Define $a_{u_{i}}=d_{u_{i}}^{+}-d_{u_{i}}^{-}$ and $b_{v_{j}}=d_{v_{j}}^{+}-d_{v_{j}}^{-}$ respectively as the imbalances of vertices $u_i$ in $U$ and $v_j$ in $V$. In this paper, we obtain constructive and existence criteria for a pair of sequences of integers to be the imbalances of some oriented bipartite graph. We also show the existence of a bipartite oriented graph with given imbalance set. 
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U. Samee; T. A. Chishti. On imbalances in oriented bipartite graphs. Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 136-141. http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a9/

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