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 , under the same assumption in their paper to guarantee the existence of a partition of into common independent sets of the two matroids, we show that there exists a nearly uniform partition of into common independent sets, where the difference of the cardinalities of any two sets in 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}
}