包装混合的高乔木

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2023-11-01 DOI:10.1016/j.disopt.2023.100811

Zoltán Szigeti

{"title":"包装混合的高乔木","authors":"Zoltán Szigeti","doi":"10.1016/j.disopt.2023.100811","DOIUrl":null,"url":null,"abstract":"<div>The aim of this paper is twofold. We first provide a new orientation theorem which gives a natural and simple proof of a result of Gao and Yang (2021) on matroid-reachability-based packing of mixed arborescences in mixed graphs by reducing it to the corresponding theorem of Király (2016) on directed graphs. Moreover, we extend another result of Gao and Yang (2021) by providing a new theorem on mixed hypergraphs having a packing of mixed hyperarborescences such that their number is at least <math><mi>ℓ</mi></math> and at most <math><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>′</mo></mrow></msup></math>, each vertex belongs to exactly <math><mi>k</mi></math> of them, and each vertex <math><mi>v</mi></math> is the root of least <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math> and at most <math><mrow><mi>g</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math> of them.</div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Packing mixed hyperarborescences\",\"authors\":\"Zoltán Szigeti\",\"doi\":\"10.1016/j.disopt.2023.100811\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>The aim of this paper is twofold. We first provide a new orientation theorem which gives a natural and simple proof of a result of Gao and Yang (2021) on matroid-reachability-based packing of mixed arborescences in mixed graphs by reducing it to the corresponding theorem of Király (2016) on directed graphs. Moreover, we extend another result of Gao and Yang (2021) by providing a new theorem on mixed hypergraphs having a packing of mixed hyperarborescences such that their number is at least <math><mi>ℓ</mi></math> and at most <math><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>′</mo></mrow></msup></math>, each vertex belongs to exactly <math><mi>k</mi></math> of them, and each vertex <math><mi>v</mi></math> is the root of least <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math> and at most <math><mrow><mi>g</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math> of them.</div>\",\"PeriodicalId\":50571,\"journal\":{\"name\":\"Discrete Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1572528623000531\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Optimization","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572528623000531","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文的目的是双重的。我们首先提供了一个新的定向定理，该定理通过将Gao和Yang(2021)关于混合图中基于拟阵可达性的混合树的填充的结果简化为Király(2016)关于有向图的相应定理，给出了一个自然而简单的证明。此外，我们扩展了Gao和Yang(2021)的另一个结果，提供了一个关于混合超图的新定理，这些混合超图具有混合超树的填充，使得它们的数量至少为r，最多为r '，每个顶点恰好属于k个顶点，并且每个顶点v是它们的最小f(v)和最多g(v)的根。

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

Packing mixed hyperarborescences

The aim of this paper is twofold. We first provide a new orientation theorem which gives a natural and simple proof of a result of Gao and Yang (2021) on matroid-reachability-based packing of mixed arborescences in mixed graphs by reducing it to the corresponding theorem of Király (2016) on directed graphs. Moreover, we extend another result of Gao and Yang (2021) by providing a new theorem on mixed hypergraphs having a packing of mixed hyperarborescences such that their number is at least $ℓ$ and at most $ℓ^{'}$ , each vertex belongs to exactly $k$ of them, and each vertex $v$ is the root of least $f (v)$ and at most $g (v)$ of them.

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 Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.