Optimal bisections of directed graphs

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2023-02-08 DOI:10.1002/rsa.21175

Guanwu Liu, Jie Ma, C. Zu

引用次数: 0

Abstract

In this article, motivated by a problem of Scott [Surveys in combinatorics, 327 (2005), 95‐117.] and a conjecture of Lee et al. [Random Struct. Algorithm, 48 (2016), 147‐170.] we consider bisections of directed graphs. We prove that every directed graph with arcs and minimum semidegree at least admits a bisection in which at least arcs cross in each direction. This provides an optimal bound as well as a positive answer to a question of Hou and Wu [J. Comb. Theory B, 132 (2018), 107‐133.] in a stronger form.

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有向图的最优等分

在这篇文章中，受Scott [Surveys In combinatorics, 327(2005)， 95‐117]的一个问题的启发。和Lee等人的猜想[随机结构]。算法，48(2016)，147‐170。我们考虑有向图的等分。我们证明了每一个具有弧和最小半度的有向图至少存在一个在每个方向上至少有弧相交的平分。这提供了一个最优边界，以及一个积极的回答问题的侯和吴[J]。梳子。理论B, 32(2018)， 107‐133。以更强的形式。

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.