{"title":"分割稀疏随机图","authors":"M. Luczak, C. McDiarmid","doi":"10.1002/1098-2418(200101)18:1%3C31::AID-RSA3%3E3.0.CO;2-1","DOIUrl":null,"url":null,"abstract":"Consider partitions of the vertex set of a graph G into two sets with sizes differing by at most 1: the bisection width of G is the minimum over all such partitions of the number of ‘‘cross edges’’ between the parts. We are interested in sparse random graphs Ž . G with edge probability c n. We show that, if c ln 4, then the bisection width is n n, c n with high probability; while if c ln 4, then it is equal to 0 with high probability. There are corresponding threshold results for partitioning into any fixed number of parts. 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18, 31 38, 2001","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":"{\"title\":\"Bisecting sparse random graphs\",\"authors\":\"M. Luczak, C. McDiarmid\",\"doi\":\"10.1002/1098-2418(200101)18:1%3C31::AID-RSA3%3E3.0.CO;2-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consider partitions of the vertex set of a graph G into two sets with sizes differing by at most 1: the bisection width of G is the minimum over all such partitions of the number of ‘‘cross edges’’ between the parts. We are interested in sparse random graphs Ž . G with edge probability c n. We show that, if c ln 4, then the bisection width is n n, c n with high probability; while if c ln 4, then it is equal to 0 with high probability. There are corresponding threshold results for partitioning into any fixed number of parts. 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18, 31 38, 2001\",\"PeriodicalId\":303496,\"journal\":{\"name\":\"Random Struct. Algorithms\",\"volume\":\"3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-01-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"23\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Struct. Algorithms\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/1098-2418(200101)18:1%3C31::AID-RSA3%3E3.0.CO;2-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Struct. Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/1098-2418(200101)18:1%3C31::AID-RSA3%3E3.0.CO;2-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 23
摘要
考虑将图G的顶点集划分为两个大小相差不超过1的集合:G的平分宽度是所有这些部分之间“交叉边”数量划分的最小值。我们对稀疏随机图很感兴趣Ž。我们证明，如果c ln 4，则等分宽度为n n, c n具有高概率;如果c ln 4，那么它大概率等于0。对于划分为任意固定数量的部分，有相应的阈值结果。2001 John Wiley & Sons, Inc。随机结构。Alg。， 18, 31, 38, 2001
Consider partitions of the vertex set of a graph G into two sets with sizes differing by at most 1: the bisection width of G is the minimum over all such partitions of the number of ‘‘cross edges’’ between the parts. We are interested in sparse random graphs Ž . G with edge probability c n. We show that, if c ln 4, then the bisection width is n n, c n with high probability; while if c ln 4, then it is equal to 0 with high probability. There are corresponding threshold results for partitioning into any fixed number of parts. 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18, 31 38, 2001
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