Abstract:
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
aui = d+ui
− d−ui and bvj = d+vj
− d−vj respectively as the imbalances of vertices ui in U
and vj 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.
