On tree decompositions whose trees are minors

Autor: Blanco, Pablo, Cook, Linda, Hatzel, Meike, Hilaire, Claire, Illingworth, Freddie, McCarty, Rose
Rok vydání: 2023
Předmět:
Druh dokumentu: Working Paper
Popis: 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 $G$.
Comment: 10 pages, 2 figures
Databáze: arXiv
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