{"title":"图、拟阵和几何格","authors":"David Sachs","doi":"10.1016/S0021-9800(70)80025-4","DOIUrl":null,"url":null,"abstract":"<div><p>It is shown that two triply connected graphs are isomorphic if their associated geometric lattices are isomorphic. The notion of vertex in a graph is described in terms of irreducible hyperplanes. Finally, necessary and sufficient conditions are given that a lattice be isomorphic to the geometric lattice associated with a graph.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"9 2","pages":"Pages 192-199"},"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)80025-4","citationCount":"10","resultStr":"{\"title\":\"Graphs, matroids, and geometric lattices\",\"authors\":\"David Sachs\",\"doi\":\"10.1016/S0021-9800(70)80025-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is shown that two triply connected graphs are isomorphic if their associated geometric lattices are isomorphic. The notion of vertex in a graph is described in terms of irreducible hyperplanes. Finally, necessary and sufficient conditions are given that a lattice be isomorphic to the geometric lattice associated with a graph.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"9 2\",\"pages\":\"Pages 192-199\"},\"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)80025-4\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021980070800254\",\"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/S0021980070800254","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is shown that two triply connected graphs are isomorphic if their associated geometric lattices are isomorphic. The notion of vertex in a graph is described in terms of irreducible hyperplanes. Finally, necessary and sufficient conditions are given that a lattice be isomorphic to the geometric lattice associated with a graph.
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