HLINĚNÝ, Petr, O-joung KWON, Jan OBDRŽÁLEK a Sebastian ORDYNIAK. Tree-depth and Vertex-minors. European Journal of Combinatorics. Elsevier, 2016, roč. 56, č. 1, s. 46-56. ISSN 0195-6698. Dostupné z: https://dx.doi.org/10.1016/j.ejc.2016.03.001. |
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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, 2016, roč.~56, č.~1, s.~46-56. ISSN~0195-6698. Dostupné z: https://dx.doi.org/10.1016/j.ejc.2016.03.001.
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