关于无限图的链接和精益树分解的反例

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-07-15 DOI:10.1002/jgt.23279

Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe, Max Pitz

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引用次数: 0

摘要

Kříž和Thomas证明了树宽度k∈N的每一个（有限或无限）图都允许宽度为k的精益树分解。我们讨论了一些反例，证明了它们的结果可能推广到任意无限树宽的极限。特别地，我们构造了一个局部有限的平面连通图，它没有精益树分解。

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Counterexamples Regarding Linked and Lean Tree-Decompositions of Infinite Graphs

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Counterexamples Regarding Linked and Lean Tree-Decompositions of Infinite Graphs

Kříž and Thomas showed that every (finite or infinite) graph of tree-width $k \in N$ admits a lean tree-decomposition of width $k$ . We discuss a number of counterexamples demonstrating the limits of possible generalisations of their result to arbitrary infinite tree-width. In particular, we construct a locally finite, planar, connected graph that has no lean tree-decomposition.

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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 .