分数色度数的新特征值约束

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2023-12-27 DOI:10.1002/jgt.23071

Krystal Guo, Sam Spiro

{"title":"分数色度数的新特征值约束","authors":"Krystal Guo, Sam Spiro","doi":"10.1002/jgt.23071","DOIUrl":null,"url":null,"abstract":"<p>Given a graph <math>\n <semantics>\n <mrow>\n <mi>G</mi>\n </mrow>\n <annotation> $G$</annotation>\n </semantics></math>, we let <math>\n <semantics>\n <mrow>\n <msup>\n <mi>s</mi>\n <mo>+</mo>\n </msup>\n <mrow>\n <mo>(</mo>\n <mi>G</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation> ${s}^{+}(G)$</annotation>\n </semantics></math> denote the sum of the squares of the positive eigenvalues of the adjacency matrix of <math>\n <semantics>\n <mrow>\n <mi>G</mi>\n </mrow>\n <annotation> $G$</annotation>\n </semantics></math>, and we similarly define <math>\n <semantics>\n <mrow>\n <msup>\n <mi>s</mi>\n <mo>−</mo>\n </msup>\n <mrow>\n <mo>(</mo>\n <mi>G</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation> ${s}^{-}(G)$</annotation>\n </semantics></math>. We prove that\n\n </p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"106 1","pages":"167-181"},"PeriodicalIF":0.9000,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23071","citationCount":"0","resultStr":"{\"title\":\"New eigenvalue bound for the fractional chromatic number\",\"authors\":\"Krystal Guo, Sam Spiro\",\"doi\":\"10.1002/jgt.23071\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Given a graph <math>\\n <semantics>\\n <mrow>\\n <mi>G</mi>\\n </mrow>\\n <annotation> $G$</annotation>\\n </semantics></math>, we let <math>\\n <semantics>\\n <mrow>\\n <msup>\\n <mi>s</mi>\\n <mo>+</mo>\\n </msup>\\n <mrow>\\n <mo>(</mo>\\n <mi>G</mi>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation> ${s}^{+}(G)$</annotation>\\n </semantics></math> denote the sum of the squares of the positive eigenvalues of the adjacency matrix of <math>\\n <semantics>\\n <mrow>\\n <mi>G</mi>\\n </mrow>\\n <annotation> $G$</annotation>\\n </semantics></math>, and we similarly define <math>\\n <semantics>\\n <mrow>\\n <msup>\\n <mi>s</mi>\\n <mo>−</mo>\\n </msup>\\n <mrow>\\n <mo>(</mo>\\n <mi>G</mi>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation> ${s}^{-}(G)$</annotation>\\n </semantics></math>. We prove that\\n\\n </p>\",\"PeriodicalId\":16014,\"journal\":{\"name\":\"Journal of Graph Theory\",\"volume\":\"106 1\",\"pages\":\"167-181\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-12-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23071\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Graph Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23071\",\"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":"Journal of Graph Theory","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23071","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

给定一个图 G$G$，我们让 s+(G)${s}^{+}(G)$ 表示 G$G$ 的邻接矩阵正特征值的平方和，我们同样定义 s-(G)${s}^{-}(G)$。我们证明

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$New eigenvalue bound for the fractional chromatic number$

查看原文本刊更多论文

New eigenvalue bound for the fractional chromatic number

Given a graph $G$ , we let $s^{+} (G)$ denote the sum of the squares of the positive eigenvalues of the adjacency matrix of $G$ , and we similarly define $s^{-} (G)$ . We prove that

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

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .