{"title":"许多","authors":"H. Ruan, And YANG WANG, Jian-Ci Xiao","doi":"10.11129/9783955534257-015","DOIUrl":null,"url":null,"abstract":". In a previous work joint with Dai and Luo, we show that a connected generalized Sierpi´nski carpet (or shortly a GSC) has cut points if and only if the associated n -th Hata graph has a long tail for all n ≥ 2. In this paper, we extend the above result by showing that it suffices to check a finite number of those graphs to reach a conclusion. This criterion provides a truly “algorithmic” solution to the cut point problem of connected GSCs. We also construct for each m ≥ 1 a connected GSC with exactly m cut points and demonstrate that when m ≥ 2, such a GSC must be of the so-called fragile type.","PeriodicalId":185294,"journal":{"name":"Robotic Building","volume":"312 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Many\",\"authors\":\"H. Ruan, And YANG WANG, Jian-Ci Xiao\",\"doi\":\"10.11129/9783955534257-015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In a previous work joint with Dai and Luo, we show that a connected generalized Sierpi´nski carpet (or shortly a GSC) has cut points if and only if the associated n -th Hata graph has a long tail for all n ≥ 2. In this paper, we extend the above result by showing that it suffices to check a finite number of those graphs to reach a conclusion. This criterion provides a truly “algorithmic” solution to the cut point problem of connected GSCs. We also construct for each m ≥ 1 a connected GSC with exactly m cut points and demonstrate that when m ≥ 2, such a GSC must be of the so-called fragile type.\",\"PeriodicalId\":185294,\"journal\":{\"name\":\"Robotic Building\",\"volume\":\"312 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Robotic Building\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11129/9783955534257-015\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Robotic Building","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11129/9783955534257-015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. In a previous work joint with Dai and Luo, we show that a connected generalized Sierpi´nski carpet (or shortly a GSC) has cut points if and only if the associated n -th Hata graph has a long tail for all n ≥ 2. In this paper, we extend the above result by showing that it suffices to check a finite number of those graphs to reach a conclusion. This criterion provides a truly “algorithmic” solution to the cut point problem of connected GSCs. We also construct for each m ≥ 1 a connected GSC with exactly m cut points and demonstrate that when m ≥ 2, such a GSC must be of the so-called fragile type.
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