{"title":"随机图的阈值谱","authors":"S. Shelah, J. Spencer","doi":"10.1145/28395.28440","DOIUrl":null,"url":null,"abstract":"Let G = G(n, p) be the random graph with n vertices and edge probability p and ƒ(n, p, A) be the probability that G has A, where A is a first order property of graphs. The evolution of the random graph is discussed in terms of a spectrum of p = p(n) where ƒ(n, p, A) changes. A partial characterization of possible spectra is given. When p = n-a, a irrational, and A is any first order statement, it is shown that lim ƒ(n, p, A) = 0 or 1.","PeriodicalId":161795,"journal":{"name":"Proceedings of the nineteenth annual ACM symposium on Theory of computing","volume":"44 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1987-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Threshold spectra for random graphs\",\"authors\":\"S. Shelah, J. Spencer\",\"doi\":\"10.1145/28395.28440\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G = G(n, p) be the random graph with n vertices and edge probability p and ƒ(n, p, A) be the probability that G has A, where A is a first order property of graphs. The evolution of the random graph is discussed in terms of a spectrum of p = p(n) where ƒ(n, p, A) changes. A partial characterization of possible spectra is given. When p = n-a, a irrational, and A is any first order statement, it is shown that lim ƒ(n, p, A) = 0 or 1.\",\"PeriodicalId\":161795,\"journal\":{\"name\":\"Proceedings of the nineteenth annual ACM symposium on Theory of computing\",\"volume\":\"44 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1987-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the nineteenth annual ACM symposium on Theory of computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/28395.28440\",\"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 of the nineteenth annual ACM symposium on Theory of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/28395.28440","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
摘要
设G = G(n, p)为有n个顶点的随机图，边概率为p，而f (n, p, A)为G存在A的概率，其中A是图的一阶性质。用p = p(n)的谱来讨论随机图的演化，其中f (n, p, a)发生变化。给出了可能谱的部分表征。当p = n-a，一个无理数，且a是任意一阶命题时，证明了lim f (n, p, a) = 0或1。
Let G = G(n, p) be the random graph with n vertices and edge probability p and ƒ(n, p, A) be the probability that G has A, where A is a first order property of graphs. The evolution of the random graph is discussed in terms of a spectrum of p = p(n) where ƒ(n, p, A) changes. A partial characterization of possible spectra is given. When p = n-a, a irrational, and A is any first order statement, it is shown that lim ƒ(n, p, A) = 0 or 1.
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