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@article{1367539,
author = {Hliněný, Petr and Kwon, Oandjoung and Obdržálek, Jan and Ordyniak, Sebastian},
article_number = {1},
doi = {http://dx.doi.org/10.1016/j.ejc.2016.03.001},
keywords = {tree-depth; shrub-depth; vertex-minor; pivot-minor},
language = {eng},
issn = {0195-6698},
journal = {European Journal of Combinatorics},
title = {Tree-depth and Vertex-minors},
volume = {56},
year = {2016}
}
TY - JOUR
ID - 1367539
AU - Hliněný, Petr - Kwon, O-joung - Obdržálek, Jan - Ordyniak, Sebastian
PY - 2016
TI - Tree-depth and Vertex-minors
JF - European Journal of Combinatorics
VL - 56
IS - 1
SP - 46-56
EP - 46-56
PB - Elsevier
SN - 01956698
KW - tree-depth
KW - shrub-depth
KW - vertex-minor
KW - pivot-minor
N2 - In a recent paper Kwon and Oum (2014), 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 how a suitable adaptation of known results implies that shrub-depth is monotone under taking vertex-minors, and we prove that every graph class of bounded shrub-depth can be obtained via vertex-minors of graphs of bounded tree-depth. While we exhibit an example that pivot-minors are generally not sufficient (unlike Kwon and Oum (2014)) in the latter statement, we then prove that the bipartite graphs in every class of bounded shrub-depth can be obtained as pivot-minors of graphs of bounded tree-depth.
ER -
HLINĚNÝ, Petr, O-joung KWON, Jan OBDRŽÁLEK a Sebastian ORDYNIAK. Tree-depth and Vertex-minors. \textit{European Journal of Combinatorics}. Elsevier, roč.~56, č.~1, s.~46-56. ISSN~0195-6698. doi:10.1016/j.ejc.2016.03.001. 2016.
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