{"title":"稀疏随机图中最大的洞","authors":"Nemanja Draganic, Stefan Glock, M. Krivelevich","doi":"10.1002/rsa.21078","DOIUrl":null,"url":null,"abstract":"We show that for any d=d(n) with d0(ϵ)≤d=o(n) , with high probability, the size of a largest induced cycle in the random graph G(n,d/n) is (2±ϵ)ndlogd . This settles a long‐standing open problem in random graph theory.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"1 1","pages":"666 - 677"},"PeriodicalIF":0.9000,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The largest hole in sparse random graphs\",\"authors\":\"Nemanja Draganic, Stefan Glock, M. Krivelevich\",\"doi\":\"10.1002/rsa.21078\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that for any d=d(n) with d0(ϵ)≤d=o(n) , with high probability, the size of a largest induced cycle in the random graph G(n,d/n) is (2±ϵ)ndlogd . This settles a long‐standing open problem in random graph theory.\",\"PeriodicalId\":54523,\"journal\":{\"name\":\"Random Structures & Algorithms\",\"volume\":\"1 1\",\"pages\":\"666 - 677\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Structures & Algorithms\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1002/rsa.21078\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Structures & Algorithms","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/rsa.21078","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
We show that for any d=d(n) with d0(ϵ)≤d=o(n) , with high probability, the size of a largest induced cycle in the random graph G(n,d/n) is (2±ϵ)ndlogd . This settles a long‐standing open problem in random graph theory.
期刊介绍：
It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness.
Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.
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