{"title":"超立方体匹配的反拉姆齐数说明","authors":"Rui Li , Yuede Ma , Zhongmei Qin , Yingping Zhao","doi":"10.1016/j.amc.2024.129154","DOIUrl":null,"url":null,"abstract":"<div><div>Let <em>Q</em> be a host graph and <span><math><mi>L</mi><mo>⊆</mo><mi>Q</mi></math></span> be a subgraph. The <em>anti-Ramsey number</em> <span><math><mi>a</mi><mi>r</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>L</mi><mo>)</mo></math></span> of <em>L</em> in <em>Q</em>, is defined as the largest number <em>t</em> that allows the existence of a <em>t</em>-edge-colored <em>Q</em> which contains no rainbow <em>L</em>. In this paper, the anti-Ramsey number for matchings when the host graph is hypercube is considered and some exact results are provided.</div></div>","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Note on the anti-Ramsey number for matching in hypercubes\",\"authors\":\"Rui Li , Yuede Ma , Zhongmei Qin , Yingping Zhao\",\"doi\":\"10.1016/j.amc.2024.129154\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <em>Q</em> be a host graph and <span><math><mi>L</mi><mo>⊆</mo><mi>Q</mi></math></span> be a subgraph. The <em>anti-Ramsey number</em> <span><math><mi>a</mi><mi>r</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>L</mi><mo>)</mo></math></span> of <em>L</em> in <em>Q</em>, is defined as the largest number <em>t</em> that allows the existence of a <em>t</em>-edge-colored <em>Q</em> which contains no rainbow <em>L</em>. In this paper, the anti-Ramsey number for matchings when the host graph is hypercube is considered and some exact results are provided.</div></div>\",\"PeriodicalId\":3,\"journal\":{\"name\":\"ACS Applied Electronic Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-10-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Electronic Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0096300324006155\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324006155","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
摘要
设 Q 是主图,L⊆Q 是子图。Q 中 L 的反拉姆齐数 ar(Q,L)定义为允许不包含彩虹 L 的 t 边着色 Q 存在的最大数 t。本文考虑了主图为超立方体时匹配的反拉姆齐数,并提供了一些精确结果。
Note on the anti-Ramsey number for matching in hypercubes
Let Q be a host graph and be a subgraph. The anti-Ramsey number of L in Q, is defined as the largest number t that allows the existence of a t-edge-colored Q which contains no rainbow L. In this paper, the anti-Ramsey number for matchings when the host graph is hypercube is considered and some exact results are provided.