Rainbow subdivisions of cliques

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2023-10-25 DOI:10.1002/rsa.21186

Tao Jiang, Shoham Letzter, Abhishek Methuku, Liana Yepremyan

引用次数: 2

Abstract

Abstract We show that for every integer and large , every properly edge‐colored graph on vertices with at least edges contains a rainbow subdivision of . This is sharp up to a polylogarithmic factor. Our proof method exploits the connection between the mixing time of random walks and expansion in graphs.

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派系的彩虹分支

摘要:我们证明了对于每一个整数和大的，每一个在至少有边的顶点上的适当的有边的图包含一个彩虹细分。这是一个多对数因子。我们的证明方法利用了图中随机漫步的混合时间与展开之间的联系。

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

Random Structures & Algorithms 数学-计算机：软件工程

CiteScore

2.50

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.