English

A Note on a Nearly Uniform Partition into Common Independent Sets of Two Matroids

Combinatorics 2019-10-01 v1 Discrete Mathematics

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 EE, under the same assumption in their paper to guarantee the existence of a partition of EE into kk common independent sets of the two matroids, we show that there exists a nearly uniform partition P\mathcal{P} of EE into kk common independent sets, where the difference of the cardinalities of any two sets in P\mathcal{P} is at most one.

Keywords

Cite

@article{arxiv.1909.13261,
  title  = {A Note on a Nearly Uniform Partition into Common Independent Sets of Two Matroids},
  author = {Satoru Fujishige and Kenjiro Takazawa and Yu Yokoi},
  journal= {arXiv preprint arXiv:1909.13261},
  year   = {2019}
}