# Kristof Bérczi : Exchange distance in split matroids

**Time: **
Wed 2022-04-13 10.15 - 11.15

**Location: **
Zoom meeting ID: 654 5562 3260

**Participating: **
Kristof Bérczi (Eötvös Loránd University)

Abstract: A nice feature of split matroids is that they generalize paving

matroids, while being closed under duality and taking minors. In this

talk, we introduce the notion of elementary split matroids, a subclass

that contains all connected split matroids. We give a hypergraph

characterization of elementary split matroids in terms of independent

sets. Based on this characterization, we give an upper bound on the

minimum number of exchanges needed to transform a basis pair into

another for split matroids. As a corollary, we verify conjectures of

Gabow, White, and Farber for this large class. Being a subclass of split

matroids, our result settles the conjectures for paving matroids as well.

Joint work with Tamás Király, Tamás Schwarcz, Yutaro Yamaguchi and Yu Yokoi.

Zoom meeting ID: 654 5562 3260

Zoom link: https://kth-se.zoom.us/j/65455623260