Corpus ID: 201271493

Tree pivot-minors and linear rank-width

@article{Dabrowski2020TreePA,
  title={Tree pivot-minors and linear rank-width},
  author={Konrad K. Dabrowski and F. Dross and Jisu Jeong and M. Kant{\'e} and O. Kwon and Sang-il Oum and D. Paulusma},
  journal={ArXiv},
  year={2020},
  volume={abs/2008.00561}
}
Treewidth and its linear variant path-width play a central role for the graph minor relation. Rank-width and linear rank-width do the same for the graph pivot-minor relation. Robertson and Seymour (1983) proved that for every tree T there exists a constant cT such that every graph of path-width at least cT contains T as a minor. Motivated by this result, we examine whether for every tree T there exists a constant dT such that every graph of linear rank-width at least dT contains T as a… Expand

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References

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TLDR
It is proved that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k, and it is shown that bipartite graphs ofRank- width at most 1 are exactly pivot- Minors of trees and bipartITE graphs of linear rank- Width 1 are precisely pivot-Minors of paths. Expand
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TLDR
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TLDR
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TLDR
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TLDR
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