## 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.

Bibtex entry:

@techreport{egres-16-10,
AUTHOR = {B{\'e}rczi, Krist{\'o}f and Frank, Andr{\'a}s},
TITLE = {Supermodularity in unweighted graph optimization II: Matroidal term rank augmentation},
NOTE= {{\tt www.cs.elte.hu/egres}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2016},
NUMBER = {TR-2016-10}
}