On tree decompositions whose trees are minors-Reference-Cited by-同舟云学术

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On tree decompositions whose trees are minors

Published:2024-02-11 Issue:2 Volume:106 Page:296-306
ISSN:0364-9024
Container-title:Journal of Graph Theory
language:en
Short-container-title:Journal of Graph Theory

Author:

Blanco Pablo¹^ORCID,Cook Linda²^ORCID,Hatzel Meike³^ORCID,Hilaire Claire⁴^ORCID,Illingworth Freddie⁵^ORCID,McCarty Rose¹^ORCID

Affiliation:

1. Department of Mathematics Princeton University Princeton New Jersey USA

2. Discrete Math Group Institute for Basic Science Daejeon Republic of Korea

3. National Institute of Informatics Tokyo Japan

4. LaBRI Université de Bordeaux Bordeaux France

5. Department of Mathematics University College London London UK

Abstract

AbstractIn 2019, Dvořák asked whether every connected graph has a tree decomposition so that is a subgraph of and the width of is bounded by a function of the treewidth of . We prove that this is false, even when has treewidth 2 and is allowed to be a minor of .

Funder

Institute for Basic Science

Engineering and Physical Sciences Research Council

National Science Foundation

Publisher

Wiley

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/jgt.23083

Reference16 articles.

1. Quickly excluding a forest

2. M.Briański G.Joret K.Majewski P.Micek M.Seweryn andR.Sharma Treedepth vs circumference arXiv:2211.11410 2022.

3. Polynomial Bounds for the Grid-Minor Theorem

4. Towards tight(er) bounds for the Excluded Grid Theorem

5. Improved Bounds for the Excluded-Minor Approximation of Treedepth

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