{"title":"Spanning -cycles in random graphs","authors":"Alberto Espuny Díaz, Y. Person","doi":"10.1017/s0963548323000172","DOIUrl":null,"url":null,"abstract":"\n We extend a recent argument of Kahn, Narayanan and Park ((2021) Proceedings of the AMS 149 3201–3208) about the threshold for the appearance of the square of a Hamilton cycle to other spanning structures. In particular, for any spanning graph, we give a sufficient condition under which we may determine its threshold. As an application, we find the threshold for a set of cyclically ordered copies of \n \n \n \n$C_4$\n\n \n that span the entire vertex set, so that any two consecutive copies overlap in exactly one edge and all overlapping edges are disjoint. This answers a question of Frieze. We also determine the threshold for edge-overlapping spanning \n \n \n \n$K_r$\n\n \n -cycles.","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":"70 11","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Combinatorics, Probability and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s0963548323000172","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 extend a recent argument of Kahn, Narayanan and Park ((2021) Proceedings of the AMS 149 3201–3208) about the threshold for the appearance of the square of a Hamilton cycle to other spanning structures. In particular, for any spanning graph, we give a sufficient condition under which we may determine its threshold. As an application, we find the threshold for a set of cyclically ordered copies of
$C_4$
that span the entire vertex set, so that any two consecutive copies overlap in exactly one edge and all overlapping edges are disjoint. This answers a question of Frieze. We also determine the threshold for edge-overlapping spanning
$K_r$
-cycles.
我们将Kahn, Narayanan和Park ((2021) Proceedings of the AMS 149 3201-3208)最近关于Hamilton循环平方出现的阈值的论点扩展到其他跨越结构。特别地，对于任意生成图，我们给出了一个确定其阈值的充分条件。作为一个应用，我们找到了一组循环有序的C_4$副本的阈值，这些副本张成整个顶点集，使得任意两个连续的副本恰好在一条边重叠，并且所有重叠的边都是不相交的。这回答了弗里兹的一个问题。我们还确定了跨越$K_r$ -环的边缘重叠的阈值。
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