%0 Journal Article
%T Graphs of Small Rank-width are Pivot-minors of Graphs of Small Tree-width
%A O-joung Kwon
%A Sang-il Oum
%J Computer Science
%D 2012
%I arXiv
%R 10.1016/j.dam.2013.01.007
%X 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.
%U http://arxiv.org/abs/1203.3606v2