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.
Prof. Charlie Jacobson, Department of Mathematics, Elmira College
"Bounds for elements of the degree sequence of an unknown vertex set in a balanced bipartite graph,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 14
, Article 11.
Available at: https://scholar.rose-hulman.edu/rhumj/vol14/iss1/11