最大权重定向切分的界限

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-08-29 DOI:10.1137/23m1567394

Jiangdong Ai, Stefanie Gerke, Gregory Gutin, Anders Yeo, Yacong Zhou

{"title":"最大权重定向切分的界限","authors":"Jiangdong Ai, Stefanie Gerke, Gregory Gutin, Anders Yeo, Yacong Zhou","doi":"10.1137/23m1567394","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2370-2391, September 2024. <br/> Abstract. We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses. We compare our results with those obtained for the maximum size of a directed cut in unweighted digraphs. In particular, we show that a lower bound obtained by Alon, Bollobás, Gyárfás, Lehel, and Scott [J. Graph Theory, 55 (2007), pp. 1–13] for unweighted acyclic digraphs can be extended to weighted digraphs with the maximum length of a cycle being bounded by a constant and the weight of every arc being at least one. We state a number of open problems.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bounds on Maximum Weight Directed Cut\",\"authors\":\"Jiangdong Ai, Stefanie Gerke, Gregory Gutin, Anders Yeo, Yacong Zhou\",\"doi\":\"10.1137/23m1567394\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2370-2391, September 2024. <br/> Abstract. We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses. We compare our results with those obtained for the maximum size of a directed cut in unweighted digraphs. In particular, we show that a lower bound obtained by Alon, Bollobás, Gyárfás, Lehel, and Scott [J. Graph Theory, 55 (2007), pp. 1–13] for unweighted acyclic digraphs can be extended to weighted digraphs with the maximum length of a cycle being bounded by a constant and the weight of every arc being at least one. We state a number of open problems.\",\"PeriodicalId\":49530,\"journal\":{\"name\":\"SIAM Journal on Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1567394\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1567394","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 离散数学杂志》，第 38 卷，第 3 期，第 2370-2391 页，2024 年 9 月。摘要我们得到了加权数图和加权非循环数图类以及它们的一些子类中的有向切分的最大权重的下限和上限。我们将我们的结果与非加权数图中有向切分最大尺寸的结果进行了比较。特别是，我们证明了 Alon、Bollobás、Gyárfás、Lehel 和 Scott [J. Graph Theory, 55 (2007), pp.我们提出了一些悬而未决的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Bounds on Maximum Weight Directed Cut

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2370-2391, September 2024.
Abstract. We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses. We compare our results with those obtained for the maximum size of a directed cut in unweighted digraphs. In particular, we show that a lower bound obtained by Alon, Bollobás, Gyárfás, Lehel, and Scott [J. Graph Theory, 55 (2007), pp. 1–13] for unweighted acyclic digraphs can be extended to weighted digraphs with the maximum length of a cycle being bounded by a constant and the weight of every arc being at least one. We state a number of open problems.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.