{"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}
引用次数: 3
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