Abstract

The present note is a strengthening of a recent paper by K. Takazawa and Y. Yokoi (A generalized-polymatroid approach to disjoint common independent sets in two matroids, Discrete Mathematics (2019)). For given two matroids on $E$, under the same assumption in their paper to guarantee the existence of a partition of $E$ into $k$ common independent sets of the two matroids, we show that there exists a nearly uniform partition $\mathcal{P}$ of $E$ into $k$ common independent sets, where the difference of the cardinalities of any two sets in $\mathcal{P}$ is at most one.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call