关于L-Grundy序列的长度

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Rebekah Herrman , Stephen G.Z. Smith
{"title":"关于L-Grundy序列的长度","authors":"Rebekah Herrman ,&nbsp;Stephen G.Z. Smith","doi":"10.1016/j.disopt.2022.100725","DOIUrl":null,"url":null,"abstract":"<div><p>An L-sequence of a graph <span><math><mi>G</mi></math></span> is a sequence of distinct vertices <span><math><mrow><mi>S</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> such that <span><math><mrow><mi>N</mi><mrow><mo>[</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>]</mo></mrow><mo>∖</mo><msubsup><mrow><mo>∪</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msubsup><mi>N</mi><mrow><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo></mrow><mo>≠</mo><mo>0̸</mo></mrow></math></span>. The length of a longest L-sequence is called the L-Grundy domination number, denoted <span><math><mrow><msubsup><mrow><mi>γ</mi></mrow><mrow><mi>g</mi><mi>r</mi></mrow><mrow><mi>L</mi></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. In this paper, we prove <span><math><mrow><msubsup><mrow><mi>γ</mi></mrow><mrow><mi>g</mi><mi>r</mi></mrow><mrow><mi>L</mi></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mi>n</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><mi>δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow></math></span>, which was conjectured by Brešar, Gologranc, Henning, and Kos. We also prove some initial results about characteristics of <span><math><mi>n</mi></math></span>-vertex graphs satisfying <span><math><mrow><msubsup><mrow><mi>γ</mi></mrow><mrow><mi>g</mi><mi>r</mi></mrow><mrow><mi>L</mi></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><mi>n</mi></mrow></math></span>.</p></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On the length of L-Grundy sequences\",\"authors\":\"Rebekah Herrman ,&nbsp;Stephen G.Z. Smith\",\"doi\":\"10.1016/j.disopt.2022.100725\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>An L-sequence of a graph <span><math><mi>G</mi></math></span> is a sequence of distinct vertices <span><math><mrow><mi>S</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> such that <span><math><mrow><mi>N</mi><mrow><mo>[</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>]</mo></mrow><mo>∖</mo><msubsup><mrow><mo>∪</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msubsup><mi>N</mi><mrow><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo></mrow><mo>≠</mo><mo>0̸</mo></mrow></math></span>. The length of a longest L-sequence is called the L-Grundy domination number, denoted <span><math><mrow><msubsup><mrow><mi>γ</mi></mrow><mrow><mi>g</mi><mi>r</mi></mrow><mrow><mi>L</mi></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. In this paper, we prove <span><math><mrow><msubsup><mrow><mi>γ</mi></mrow><mrow><mi>g</mi><mi>r</mi></mrow><mrow><mi>L</mi></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mi>n</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><mi>δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow></math></span>, which was conjectured by Brešar, Gologranc, Henning, and Kos. We also prove some initial results about characteristics of <span><math><mi>n</mi></math></span>-vertex graphs satisfying <span><math><mrow><msubsup><mrow><mi>γ</mi></mrow><mrow><mi>g</mi><mi>r</mi></mrow><mrow><mi>L</mi></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><mi>n</mi></mrow></math></span>.</p></div>\",\"PeriodicalId\":50571,\"journal\":{\"name\":\"Discrete Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1572528622000342\",\"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/S1572528622000342","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: 2

摘要

图G的l序列是由不同顶点S=(v1,…,vk)组成的序列,使得N[vi]∈∪j=1i−1N(vj)≠0 ε。最长l序列的长度称为L-Grundy支配数,记为γgrL(G)。本文证明了Brešar、Gologranc、Henning和Kos猜想的γgrL(G)≤n(G)−δ(G)+1。我们还证明了n顶点图满足γgrL(G)=n的一些初步结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the length of L-Grundy sequences

An L-sequence of a graph G is a sequence of distinct vertices S=(v1,,vk) such that N[vi]j=1i1N(vj). The length of a longest L-sequence is called the L-Grundy domination number, denoted γgrL(G). In this paper, we prove γgrL(G)n(G)δ(G)+1, which was conjectured by Brešar, Gologranc, Henning, and Kos. We also prove some initial results about characteristics of n-vertex graphs satisfying γgrL(G)=n.

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
Discrete Optimization 管理科学-应用数学
CiteScore
2.10
自引率
9.10%
发文量
30
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信