Tree-depth and Vertex-minors

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F16%3A00088544" target="_blank" >RIV/00216224:14330/16:00088544 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ejc.2016.03.001" target="_blank" >http://dx.doi.org/10.1016/j.ejc.2016.03.001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2016.03.001" target="_blank" >10.1016/j.ejc.2016.03.001</a>

Result language
angličtina
Original language name
Tree-depth and Vertex-minors
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Project
<a href="/en/project/GA14-03501S" target="_blank" >GA14-03501S: Parameterized algorithms and kernelization in the context of discrete mathematics and logic</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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