Tree-depth and Vertex-minors
Discrete Mathematics
2014-03-28 v1 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1403.7024,
title = {Tree-depth and Vertex-minors},
author = {Petr Hliněný and O-joung Kwon and Jan Obdržálek and Sebastian Ordyniak},
journal= {arXiv preprint arXiv:1403.7024},
year = {2014}
}