可整除细分的紧界

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-16 DOI:10.1016/j.jctb.2023.10.011

Shagnik Das , Nemanja Draganić , Raphael Steiner

引用次数: 1

摘要

Alon和Krivelevich证明了对于每一个n顶点次三次图H和每一个整数q≥2，存在一个(最小)整数f=f(H,q)，使得每一个Kf-minor都包含H的一个细分，其中每个细分路径的长度都可以被q整除。改进了他们的超指数界，证明了f(H,q)≤212qn+8n+14q是最优的，直到一个常数乘因子。

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Tight bounds for divisible subdivisions

Alon and Krivelevich proved that for every n-vertex subcubic graph H and every integer $q \geq 2$ there exists a (smallest) integer $f = f (H, q)$ such that every $K_{f}$ -minor contains a subdivision of H in which the length of every subdivision-path is divisible by q. Improving their superexponential bound, we show that $f (H, q) \leq \frac{21}{2} q n + 8 n + 14 q$ , which is optimal up to a constant multiplicative factor.

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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.