最大度数较大的树的拉姆齐数与车轮图 $W_8$$ 的比较

IF 1 3区数学 Q1 MATHEMATICS

Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-06-26 DOI:10.1007/s40840-024-01733-0

Zhi Yee Chng, Thomas Britz, Ta Sheng Tan, Kok Bin Wong

{"title":"最大度数较大的树的拉姆齐数与车轮图 $W_8$$ 的比较","authors":"Zhi Yee Chng, Thomas Britz, Ta Sheng Tan, Kok Bin Wong","doi":"10.1007/s40840-024-01733-0","DOIUrl":null,"url":null,"abstract":"The Ramsey numbers \$R(T_n,W_8)\$ are determined for each tree graph \$T_n\$ of order \$n\\ge 7\$ and maximum degree \$\\Delta (T_n)\$ equal to either \$n-4\$ or \$n-5\$. These numbers indicate strong support for the conjecture, due to Chen, Zhang and Zhang and to Hafidh and Baskoro, that \$R(T_n,W_m) = 2n-1\$ for each tree graph \$T_n\$ of order \$n\\ge m-1\$ with \$\\Delta (T_n)\\le n-m+2\$ when \$m\\ge 4\$ is even.","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"13 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph $$W_8$$\",\"authors\":\"Zhi Yee Chng, Thomas Britz, Ta Sheng Tan, Kok Bin Wong\",\"doi\":\"10.1007/s40840-024-01733-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Ramsey numbers \\\$R(T_n,W_8)\\\$ are determined for each tree graph \\\$T_n\\\$ of order \\\$n\\\\ge 7\\\$ and maximum degree \\\$\\\\Delta (T_n)\\\$ equal to either \\\$n-4\\\$ or \\\$n-5\\\$. These numbers indicate strong support for the conjecture, due to Chen, Zhang and Zhang and to Hafidh and Baskoro, that \\\$R(T_n,W_m) = 2n-1\\\$ for each tree graph \\\$T_n\\\$ of order \\\$n\\\\ge m-1\\\$ with \\\$\\\\Delta (T_n)\\\\le n-m+2\\\$ when \\\$m\\\\ge 4\\\$ is even.\",\"PeriodicalId\":50718,\"journal\":{\"name\":\"Bulletin of the Malaysian Mathematical Sciences Society\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Malaysian Mathematical Sciences Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40840-024-01733-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Malaysian Mathematical Sciences Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40840-024-01733-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

拉姆齐数$R(T_n,W_8)$是为每个树图秩为$n\ge 7$ 和最大度为$\Delta (T_n)$等于$n-4$或$n-5$的树图$T_n$确定的。这些数字表明，陈、张和张以及哈菲德和巴斯克罗的猜想得到了强有力的支持，即当（m/ge 4\) 是偶数时，对于每个阶为（n/ge m-1）的树图（T_n）来说，（R(T_n,W_m) = 2n-1/）具有（\Delta (T_n)\le n-m+2/）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph $$W_8$$

查看原文本刊更多论文

The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph $$W_8$$

The Ramsey numbers $R(T_n,W_8)$ are determined for each tree graph $T_n$ of order $n\ge 7$ and maximum degree $\Delta (T_n)$ equal to either $n-4$ or $n-5$. These numbers indicate strong support for the conjecture, due to Chen, Zhang and Zhang and to Hafidh and Baskoro, that $R(T_n,W_m) = 2n-1$ for each tree graph $T_n$ of order $n\ge m-1$ with $\Delta (T_n)\le n-m+2$ when $m\ge 4$ is even.

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

Bulletin of the Malaysian Mathematical Sciences Society 数学-数学

CiteScore

2.40

自引率

8.30%

发文量

176

审稿时长

3 months

期刊介绍： This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.