Combinatorial $n$-od covers of graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913892600381440 |
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| author | Hoehn, Logan C. Maldonado-Garcia, Hugo Adrian |
| author_facet | Hoehn, Logan C. Maldonado-Garcia, Hugo Adrian |
| contents | We introduce the notion of a combinatorial $n$-od cover, for $n \geq 3$, which is a tool that may be used to show that certain continua embedded in the plane are not simple $n$-od-like. Using this tool, we generalize a classic example of Ingram, and give a construction, for each $n \geq 3$, of an indecomposable plane continuum which is simple $(n+1)$-od-like but not simple $n$-od-like, and such that each non-degenerate proper subcontinuum is an arc. These examples may be compared with related constructions of Kennaugh [10]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial $n$-od covers of graphs Hoehn, Logan C. Maldonado-Garcia, Hugo Adrian General Topology Primary 54F15, Secondary 54C25, 54F50 We introduce the notion of a combinatorial $n$-od cover, for $n \geq 3$, which is a tool that may be used to show that certain continua embedded in the plane are not simple $n$-od-like. Using this tool, we generalize a classic example of Ingram, and give a construction, for each $n \geq 3$, of an indecomposable plane continuum which is simple $(n+1)$-od-like but not simple $n$-od-like, and such that each non-degenerate proper subcontinuum is an arc. These examples may be compared with related constructions of Kennaugh [10]. |
| title | Combinatorial $n$-od covers of graphs |
| topic | General Topology Primary 54F15, Secondary 54C25, 54F50 |
| url | https://arxiv.org/abs/2506.11979 |