织布机

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-26 DOI:10.1016/j.disc.2024.114181

{"title":"织布机","authors":"","doi":"10.1016/j.disc.2024.114181","DOIUrl":null,"url":null,"abstract":"<div>A pair <math><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math> of hypergraphs is called orthogonal if <math><mo>|</mo><mi>a</mi><mo>∩</mo><mi>b</mi><mo>|</mo><mo>=</mo><mn>1</mn></math> for every pair of edges <math><mi>a</mi><mo>∈</mo><mi>A</mi><mo>,</mo><mspace></mspace><mi>b</mi><mo>∈</mo><mi>B</mi></math>. An orthogonal pair of hypergraphs is called a loom if each of its two members is the set of minimum covers of the other. Looms appear naturally in the context of a conjecture of Gyárfás and Lehel on the covering number of cross-intersecting hypergraphs. We study their properties and ways of construction, and prove special cases of a conjecture that if true would imply the Gyárfás–Lehel conjecture.</div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Looms\",\"authors\":\"\",\"doi\":\"10.1016/j.disc.2024.114181\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>A pair <math><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math> of hypergraphs is called orthogonal if <math><mo>|</mo><mi>a</mi><mo>∩</mo><mi>b</mi><mo>|</mo><mo>=</mo><mn>1</mn></math> for every pair of edges <math><mi>a</mi><mo>∈</mo><mi>A</mi><mo>,</mo><mspace></mspace><mi>b</mi><mo>∈</mo><mi>B</mi></math>. An orthogonal pair of hypergraphs is called a loom if each of its two members is the set of minimum covers of the other. Looms appear naturally in the context of a conjecture of Gyárfás and Lehel on the covering number of cross-intersecting hypergraphs. We study their properties and ways of construction, and prove special cases of a conjecture that if true would imply the Gyárfás–Lehel conjecture.</div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24003121\",\"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":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24003121","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

如果每对边 a∈A,b∈B 的|a∩b|=1，则一对 (A,B) 超图称为正交。如果一对正交的超图中的每一个成员都是另一个成员的最小覆盖集，那么这对超图就叫做织布机。织布机很自然地出现在 Gyárfás 和 Lehel 关于交叉相交超图覆盖数的猜想中。我们研究了它们的性质和构造方法，并证明了一个猜想的特例，如果该猜想成立，则意味着 Gyárfás-Lehel 猜想成立。

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

Looms

A pair $(A, B)$ of hypergraphs is called orthogonal if $| a \cap b | = 1$ for every pair of edges $a \in A, b \in B$ . An orthogonal pair of hypergraphs is called a loom if each of its two members is the set of minimum covers of the other. Looms appear naturally in the context of a conjecture of Gyárfás and Lehel on the covering number of cross-intersecting hypergraphs. We study their properties and ways of construction, and prove special cases of a conjecture that if true would imply the Gyárfás–Lehel conjecture.

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.