{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"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\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23071\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23071","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0