{"title":"The random bipartite nearest neighbor graphs","authors":"B. Pittel, Robert S. Weishaar","doi":"10.1002/(SICI)1098-2418(199910/12)15:3/4%3C279::AID-RSA6%3E3.0.CO;2-J","DOIUrl":null,"url":null,"abstract":"The bipartite kth nearest neighbor graphs B are studied. It is shown that B k 1 has a limiting expected matching number of approximately 80% of its vertices, that with high Ž . probability whp B has at least 2 log nr13 log log n vertices not matched, and that whp B 2 3 does have a perfect matching. We also find a formula for the limiting probability that B is 2 connected and show that whp B is connected. Q 1999 John Wiley & Sons, Inc. Random Struct. 3 Alg., 15, 279]310, 1999","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"18 9-10","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Struct. Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/(SICI)1098-2418(199910/12)15:3/4%3C279::AID-RSA6%3E3.0.CO;2-J","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
Abstract
The bipartite kth nearest neighbor graphs B are studied. It is shown that B k 1 has a limiting expected matching number of approximately 80% of its vertices, that with high Ž . probability whp B has at least 2 log nr13 log log n vertices not matched, and that whp B 2 3 does have a perfect matching. We also find a formula for the limiting probability that B is 2 connected and show that whp B is connected. Q 1999 John Wiley & Sons, Inc. Random Struct. 3 Alg., 15, 279]310, 1999
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