Description
Abstract:
In our joint work with Kristóf Bérczi and Yutaro Yamaguchi, we made the following conjecture: if M=(S,I) is a matroid in which S can be partitioned into k independent sets, then there exists a partition matroid N=(S,J) with J\subseteq I, in which S can be partitioned into 2k independent sets. If true, this conjecture implies the topological result of Aharoni and Berger about covering with common independent sets of two matroids, as well as an upper bound on the list coloring number of the intersection of two matroids. We proved that the conjecture holds for paving matroids, graphic matroids and gammoids. I will present some of these results.
The talk will be in English.
Please contact Tamás Király (tkiraly[at]cs.elte.hu) for Zoom access if you are not on the mailing list.