Bipartite-assembly

Abstract

Let A and B be nonempty sets of positive integers. We study the problem of finding bipartite graphs G with bipartition sets X and Y such that every element in A is the degree of at least one vertex in X and every element of B is the degree of at least one vertex in Y. In addition to the question of existence the problem of determining the minimum order and size of graphs that are realizable for a given A and B is considered.