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Article: On the existence of cut points of connected generalized Sierpinski carpets

TitleOn the existence of cut points of connected generalized Sierpinski carpets
Authors
Ruan, Huo JunWang, YangXiao, Jian Ci
Keywordsconnectedness
cut points
Generalized Sierpinski carpets
Hata graphs
Issue Date2023
Citation
Annales Fennici Mathematici, 2023, v. 48, n. 1, p. 229-254 How to Cite?
DOI: http://dx.doi.org/10.54330/afm.127049
AbstractIn a previous work joint with Dai and Luo, we show that a connected generalized Sierpinski 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 non-fragile type
Persistent Identifierhttp://hdl.handle.net/10722/363520
ISSN
2737-0690
2023 Impact Factor: 0.9
2023 SCImago Journal Rankings: 0.862

 

DC FieldValueLanguage
dc.contributor.authorRuan, Huo Jun-
dc.contributor.authorWang, Yang-
dc.contributor.authorXiao, Jian Ci-
dc.date.accessioned2025-10-10T07:47:31Z-
dc.date.available2025-10-10T07:47:31Z-
dc.date.issued2023-
dc.identifier.citationAnnales Fennici Mathematici, 2023, v. 48, n. 1, p. 229-254-
dc.identifier.issn2737-0690-
dc.identifier.urihttp://hdl.handle.net/10722/363520-
dc.description.abstractIn a previous work joint with Dai and Luo, we show that a connected generalized Sierpinski 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 non-fragile type-
dc.languageeng-
dc.relation.ispartofAnnales Fennici Mathematici-
dc.subjectconnectedness-
dc.subjectcut points-
dc.subjectGeneralized Sierpinski carpets-
dc.subjectHata graphs-
dc.titleOn the existence of cut points of connected generalized Sierpinski carpets-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.54330/afm.127049-
dc.identifier.scopuseid_2-s2.0-85150414798-
dc.identifier.volume48-
dc.identifier.issue1-
dc.identifier.spage229-
dc.identifier.epage254-
dc.identifier.eissn2737-114X-

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