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On tree decompositions whose trees are minors

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Title
On tree decompositions whose trees are minors
Author(s)
Blanco, Pablo; Linda Cook; Hatzel, Meike; Hilaire, Claire; Illingworth, Freddie; McCarty, Rose
Publication Date
2024-06
Journal
Journal of Graph Theory, v.106, no.2, pp.296 - 306
Publisher
John Wiley & Sons Inc.
Abstract
In 2019, Dvorak asked whether every connected graph G $G$ has a tree decomposition ( T , B ) $(T,{\rm{ {\mathcal B} }})$ so that T $T$ is a subgraph of G $G$ and the width of ( T , B ) $(T,{\rm{ {\mathcal B} }})$ is bounded by a function of the treewidth of G $G$. We prove that this is false, even when G $G$ has treewidth 2 and T $T$ is allowed to be a minor of G $G$.
URI
https://pr.ibs.re.kr/handle/8788114/15119
DOI
10.1002/jgt.23083
ISSN
0364-9024
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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