{"title":"吉尔伯特随机图的零一定律","authors":"G. McColm","doi":"10.1109/LICS.1996.561448","DOIUrl":null,"url":null,"abstract":"We look at a competitor of the Erdos-Renyi models of random graphs, one proposed by E. Gilbert (1961): given /spl delta/>0 and a metric space X of diameter >/spl delta/, scatter n vertices at random on X and connect those of distance </spl delta/ apart: we get a random graph G/sub n,/spl delta///sup X/. Question: for fixed X, /spl delta/, do we have 0-1 laws for FO logic? We prove that this is true if X is a circle.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"62 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Zero-one laws for Gilbert random graphs\",\"authors\":\"G. McColm\",\"doi\":\"10.1109/LICS.1996.561448\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We look at a competitor of the Erdos-Renyi models of random graphs, one proposed by E. Gilbert (1961): given /spl delta/>0 and a metric space X of diameter >/spl delta/, scatter n vertices at random on X and connect those of distance </spl delta/ apart: we get a random graph G/sub n,/spl delta///sup X/. Question: for fixed X, /spl delta/, do we have 0-1 laws for FO logic? We prove that this is true if X is a circle.\",\"PeriodicalId\":382663,\"journal\":{\"name\":\"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science\",\"volume\":\"62 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1996-07-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/LICS.1996.561448\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.1996.561448","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We look at a competitor of the Erdos-Renyi models of random graphs, one proposed by E. Gilbert (1961): given /spl delta/>0 and a metric space X of diameter >/spl delta/, scatter n vertices at random on X and connect those of distance