Refining Tree-Decompositions so That They Display the k-Blocks

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-02-10 DOI:10.1002/jgt.23230

Sandra Albrechtsen

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引用次数: 0

Abstract

Carmesin and Gollin proved that every finite graph has a canonical tree-decomposition $(T, V)$ of adhesion less than $k$ that efficiently distinguishes every two distinct $k$ -profiles, and which has the further property that every separable $k$ -block is equal to the unique part of $(T, V)$ in which it is contained. We give a shorter proof of this result by showing that such a tree-decomposition can in fact be obtained from any canonical tight tree-decomposition of adhesion less than $k$ . For this, we decompose the parts of such a tree-decomposition by further tree-decompositions. As an application, we also obtain a generalization of Carmesin and Gollin's result to locally finite graphs.

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改进树分解，使它们显示k块

Carmesin和Gollin证明了每个有限图都有一个正则树分解(T，V)的附着力小于k，有效地区分每两个不同的k - 概要文件,它还有一个进一步的性质，即每一个可分离的k块都等于(T)的唯一部分， V)它被包含在其中。我们通过证明这样的树分解实际上可以从任何小于k的附着力正则紧树分解中得到，从而给出了这个结果的一个简短的证明。为此，我们通过进一步的树分解来分解这种树分解的各个部分。作为应用，我们也得到了Carmesin和Gollin结果在局部有限图上的推广。

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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 .