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arXiv · 1403.7024

Tree-depth and Vertex-minors

Petr Hliněný·O-joung Kwon·Jan Obdržálek·Sebastian Ordyniak
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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.

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Petr Hliněný, O-joung Kwon, Jan Obdržálek, Sebastian Ordyniak. 2014-03-27. Tree-depth and Vertex-minors. https://arxiv.org/abs/1403.7024

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