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Tree-depth and vertex-minors.
- Source :
-
European Journal of Combinatorics . Aug2016, Vol. 56, p46-56. 11p. - Publication Year :
- 2016
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *TREE graphs
*GRAPH theory
*MATHEMATICAL bounds
*MATHEMATICAL proofs
*SET theory
Subjects
Details
- Language :
- English
- ISSN :
- 01956698
- Volume :
- 56
- Database :
- Academic Search Index
- Journal :
- European Journal of Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 114847186
- Full Text :
- https://doi.org/10.1016/j.ejc.2016.03.001