{"title":"图形的邻里平衡着色","authors":"Bryan Freyberg, Alison Marr","doi":"10.1007/s00373-024-02766-9","DOIUrl":null,"url":null,"abstract":"<p>Given a simple graph <i>G</i>, we ask when <i>V</i>(<i>G</i>) may be partitioned into two sets such that every vertex has an equal number of neighbors from each set. We establish a number of results for common families of graphs and completely classify 4-regular circulants which posses this property.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Neighborhood Balanced Colorings of Graphs\",\"authors\":\"Bryan Freyberg, Alison Marr\",\"doi\":\"10.1007/s00373-024-02766-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Given a simple graph <i>G</i>, we ask when <i>V</i>(<i>G</i>) may be partitioned into two sets such that every vertex has an equal number of neighbors from each set. We establish a number of results for common families of graphs and completely classify 4-regular circulants which posses this property.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00373-024-02766-9\",\"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://doi.org/10.1007/s00373-024-02766-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Given a simple graph G, we ask when V(G) may be partitioned into two sets such that every vertex has an equal number of neighbors from each set. We establish a number of results for common families of graphs and completely classify 4-regular circulants which posses this property.
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