Supermodularity in Unweighted Graph Optimization II: Matroidal Term Rank Augmentation

Abstract

Ryser's max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with matching number at least $\ell$. In a previous paper by the authors, a generalization was developed for the case when the degrees are constrained by upper and lower bounds. Here two other extensions of Ryser's theorem are discussed. The first one is a matroidal model, while the second one settles the augmentation version. In fact, the two directions shall be integrated into one single framework.