Consider the set of all balanced bipartite graphs. Given the degree sequence of one vertex set in one of these graphs, we find bounds for any given position in the degree sequence of the unknown vertex set. Additionally, we establish bounds for the median of the unknown degree sequence, as well as bounds for any given percentile. We discuss the connection between this paper and the High School Prom Theorem.

Author Bio

Sam Pine is an undergraduate mathematics and economics student at Elmira College. He completed this work between his sophomore and junior year, as part of the Elmira College Summer research program. Pine plans to pursue an MS in applied mathematics upon graduating in 2014.