%0 Journal Article
%T Tree-depth and Vertex-minors
%A Petr Hlin¨§ny
%A O-joung Kwon
%A Jan Obdr£¿¨¢lek
%A Sebastian Ordyniak
%J Computer Science
%D 2014
%I arXiv
%X In a recent paper, Kwon and Oum claim that every graph of bounded rank-width is a pivot-minor of a graph of bounded tree-width (while the converse has been known true already before). We study the analogous questions for "depth" parameters of graphs, namely for the tree-depth and related new shrub-depth. We show that shrub-depth is monotone under taking vertex-minors, and that every graph class of bounded shrub-depth can be obtained via vertex-minors of graphs of bounded tree-depth. We also consider the same questions for bipartite graphs and pivot-minors.
%U http://arxiv.org/abs/1403.7024v1