{"title":"关于给定周长的正则n图的存在性","authors":"N. Sauer","doi":"10.1016/S0021-9800(70)80021-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper I construct for each <em>g, l</em>, and <em>m</em>≡0 modulo <em>n</em> a regular <em>n</em>-graph <em>G</em> of degree <em>g</em> and girth <em>l</em> with <em>m≥φ(g, l, n)</em> points, where <em>φ(g, l, n)</em> is a certain function.</p><p>In [1] Erdös constructed such graphs for <em>n</em>=2.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"9 2","pages":"Pages 144-147"},"PeriodicalIF":0.0000,"publicationDate":"1970-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80021-7","citationCount":"15","resultStr":"{\"title\":\"On the existence of regular n-graphs with given girth\",\"authors\":\"N. Sauer\",\"doi\":\"10.1016/S0021-9800(70)80021-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper I construct for each <em>g, l</em>, and <em>m</em>≡0 modulo <em>n</em> a regular <em>n</em>-graph <em>G</em> of degree <em>g</em> and girth <em>l</em> with <em>m≥φ(g, l, n)</em> points, where <em>φ(g, l, n)</em> is a certain function.</p><p>In [1] Erdös constructed such graphs for <em>n</em>=2.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"9 2\",\"pages\":\"Pages 144-147\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1970-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80021-7\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021980070800217\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021980070800217","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the existence of regular n-graphs with given girth
In this paper I construct for each g, l, and m≡0 modulo n a regular n-graph G of degree g and girth l with m≥φ(g, l, n) points, where φ(g, l, n) is a certain function.
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