Graphs of Linear Growth have Bounded Treewidth

IF 0.7 4区数学 Q2 MATHEMATICS

Electronic Journal of Combinatorics Pub Date : 2022-10-25 DOI:10.37236/11657

Rutger Campbell, Marc Distel, J. P. Gollin, Daniel J. Harvey, Kevin Hendrey, Robert Hickingbotham, B. Mohar, D. Wood

引用次数: 2

Abstract

A graph class $\mathcal{G}$ has linear growth if, for each graph $G \in \mathcal{G}$ and every positive integer $r$, every subgraph of $G$ with radius at most $r$ contains $O(r)$ vertices. In this paper, we show that every graph class with linear growth has bounded treewidth.

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线性增长图的树宽有界

一个图类$\mathcal{G}$具有线性增长，如果对于每一个图$G \in $ mathcal{G}$和每一个正整数$r$， $G$的每一个半径不超过$r$的子图包含$O(r)$顶点。本文证明了每一类具有线性增长的图都有有界树宽。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Journal of Combinatorics 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

212

审稿时长

3-6 weeks

期刊介绍： The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.