On the difference of mean subtree orders under edge contraction

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-18 DOI:10.1016/j.jctb.2024.06.002

Ruoyu Wang

引用次数: 0

Abstract

Given a tree T of order n, one can contract any edge and obtain a new tree $T^{⁎}$ of order $n - 1$ . In 1983, Jamison made a conjecture that the mean subtree order, i.e., the average order of all subtrees, decreases at least $\frac{1}{3}$ in contracting an edge of a tree. In 2023, Luo, Xu, Wagner and Wang proved the case when the edge to be contracted is a pendant edge. In this article, we prove that the conjecture is true in general.

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论边缘收缩下平均子树顺序的差异

给定一棵阶数为 n 的树 T，可以收缩任意一条边，得到一棵阶数为 n-1 的新树 T⁎。1983 年，Jamison 提出了一个猜想，即在收缩树的一条边时，平均子树序（即所有子树的平均序）至少会减少 13。2023 年，Luo、Xu、Wagner 和 Wang 证明了要收缩的边是垂边时的情况。在本文中，我们将证明该猜想在一般情况下为真。

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

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.