Corpus ID: 207779939

Obstructions for bounded shrub-depth and rank-depth

@article{Kwon2019ObstructionsFB,
  title={Obstructions for bounded shrub-depth and rank-depth},
  author={O. Kwon and R. McCarty and Sang-il Oum and P. Wollan},
  journal={ArXiv},
  year={2019},
  volume={abs/1911.00230}
}

O. Kwon, R. McCarty, +1 author P. Wollan

Published 2019

Mathematics, Computer Science

ArXiv

Shrub-depth and rank-depth are dense analogues of the tree-depth of a graph. It is well known that a graph has large tree-depth if and only if it has a long path as a subgraph. We prove an analogous statement for shrub-depth and rank-depth, which was conjectured by Hliněný, Kwon, Obdržalek, and Ordyniak [Tree-depth and vertex-minors, European J.~Combin. 2016]. Namely, we prove that a graph has large rank-depth if and only if it has a vertex-minor isomorphic to a long path. This implies that for… CONTINUE READING

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