On tree decompositions whose trees are minors

IF 1 3区数学 Q2 MATHEMATICS Journal of Graph Theory Pub Date : 2024-02-11 DOI:10.1002/jgt.23083

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

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Abstract

In 2019, Dvořák asked whether every connected graph $G$ has a tree decomposition $(T, B)$ so that $T$ is a subgraph of $G$ and the width of $(T, B)$ 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 $G$ .

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关于树为未成年人的树分解

2019 年，德沃夏克提出了一个问题：是否每个连通图 G$G$ 都有一个树分解 (T,B)$(T,{\rm{ {\mathcal B} }})$，从而 T$T$ 是 G$G$ 的子图，并且 (T,B)$(T,{\rm{ {\mathcal B} }})$ 的宽度受 G$G$ 树宽的函数约束？我们证明，即使 G$G$ 的树宽为 2 且允许 T$T$ 是 G$G$ 的次要图，这也是错误的。

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .

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