Realizing degree imbalances in directed graphs
  In a directed graph, the imbalance of a vertex is its outdegree minus its indegree. We characterize the sequences that are realizable as the sequence of imbalances of a simple directed graph. Moreover, a realization of a realizable sequence can be produced by a greedy algorithm. 
Dhruv Mubayi and Todd G. Will (Davidson College), and Douglas B. West   (Univ. of Illinois)