On tree decompositions whose trees are minors

Pablo Blanco; Linda Cook; Meike Hatzel; Claire Hilaire; Freddie Illingworth; Rose McCarty

On tree decompositions whose trees are minors

Combinatorics 2023-02-24 v1

Authors: Pablo Blanco , Linda Cook , Meike Hatzel , Claire Hilaire , Freddie Illingworth , Rose McCarty

Abstract

In 2019, Dvo\v{r}\'{a}k asked whether every connected graph $G$ has a tree decomposition $(T, \mathcal{B})$ so that $T$ is a subgraph of $G$ and the width of $(T, \mathcal{B})$ is bounded by a function of the treewidth of $G$ . We prove that this is false, even when $G$ has treewidth $2$ and $T$ is allowed to be a minor of $G$ .

Keywords

graph theory trees phylogenetic trees

Cite

@article{arxiv.2302.12106,
  title  = {On tree decompositions whose trees are minors},
  author = {Pablo Blanco and Linda Cook and Meike Hatzel and Claire Hilaire and Freddie Illingworth and Rose McCarty},
  journal= {arXiv preprint arXiv:2302.12106},
  year   = {2023}
}

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10 pages, 2 figures

On tree decompositions whose trees are minors

Abstract

Keywords

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