可整除细分的紧界

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B 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。

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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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

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

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.