Tree-depth and Vertex-minors
  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. 
Petr Hlin\v{e}n\'y, O-joung Kwon, Jan Obdr\v{z}\'alek, Sebastian   Ordyniak
cs.DM math.CO