Efficiently distinguishing all tangles in locally finite graphs

IF 1.2 1区 数学 Q1 MATHEMATICS
Raphael W. Jacobs, Paul Knappe
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引用次数: 0

Abstract

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.

有效区分局部有限图中的所有缠结
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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来源期刊
CiteScore
2.70
自引率
14.30%
发文量
99
审稿时长
6-12 weeks
期刊介绍: The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.
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