# Graphs of small rank-width are pivot-minors of graphs of small tree-width

## O-joung Kwon (KAIST, South Korea)

When: May 20, 2pm

Where: room G2.91b/G215

**Abstract**

We prove that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors of trees and bipartite graphs of linear rank-width at most 1 are precisely pivot-minors of paths