有效区分局部有限图中的所有缠结

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-03-21 DOI:10.1016/j.jctb.2024.03.004

Raphael W. Jacobs, Paul Knappe

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引用次数: 0

摘要

有限图具有能有效区分其所有纠结的树形分解，而具有粗末端的局部有限图则不需要这样的树形分解。我们证明，每一个没有粗末端的局部有限图都有这样的树形分解，事实上是一个典型的树形分解。我们的证明展示了在任何阻碍这种树形分解存在的障碍处的厚末端，并建立在分析严格递增分离序列的极限行为的新方法之上。

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Efficiently distinguishing all tangles in locally finite graphs

While finite graphs have tree-decompositions that efficiently distinguish all their tangles, locally finite graphs with thick ends need not have such tree-decompositions. We show that every locally finite graph without thick ends admits such a tree-decomposition, in fact a canonical one. Our proof exhibits a thick end at any obstruction to the existence of such tree-decompositions and builds on new methods for the analysis of the limit behaviour of strictly increasing sequences of separations.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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