{"title":"友谊定理","authors":"E. Walker","doi":"10.1017/9781108912181.011","DOIUrl":null,"url":null,"abstract":". . . in other words, if every pair of people at a party shares exactly one mutual friend at the party then some guest is a friend of everybody present. More is is true: friendships must be arranged in triangles which intersect only in the universally popular guest. So the graphs satisfying the hypothesis of the theorem are those shown on the immediate right, usually known as ‘windmill’ graphs.","PeriodicalId":179047,"journal":{"name":"The Discrete Mathematical Charms of Paul Erdős","volume":"52 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Friendship Theorem\",\"authors\":\"E. Walker\",\"doi\":\"10.1017/9781108912181.011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". . . in other words, if every pair of people at a party shares exactly one mutual friend at the party then some guest is a friend of everybody present. More is is true: friendships must be arranged in triangles which intersect only in the universally popular guest. So the graphs satisfying the hypothesis of the theorem are those shown on the immediate right, usually known as ‘windmill’ graphs.\",\"PeriodicalId\":179047,\"journal\":{\"name\":\"The Discrete Mathematical Charms of Paul Erdős\",\"volume\":\"52 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Discrete Mathematical Charms of Paul Erdős\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/9781108912181.011\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Discrete Mathematical Charms of Paul Erdős","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/9781108912181.011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. . . in other words, if every pair of people at a party shares exactly one mutual friend at the party then some guest is a friend of everybody present. More is is true: friendships must be arranged in triangles which intersect only in the universally popular guest. So the graphs satisfying the hypothesis of the theorem are those shown on the immediate right, usually known as ‘windmill’ graphs.
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