Neighborly Murai spheres and the Simplicial Steinitz Problem
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911742265655296 |
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| author | Limonchenko, Ivan Vavpetič, Aleš |
| author_facet | Limonchenko, Ivan Vavpetič, Aleš |
| contents | We provide a classification of neighborly Murai spheres, which implies that all of them are polytopal. Furthermore, we show that each neighborly $d$-sphere with no more than $d+4$ vertices is combinatorially equivalent to a Murai sphere for any $d\geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02513 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neighborly Murai spheres and the Simplicial Steinitz Problem Limonchenko, Ivan Vavpetič, Aleš Combinatorics 05E45, 13F55, 52B05, 52B12, 57S12 We provide a classification of neighborly Murai spheres, which implies that all of them are polytopal. Furthermore, we show that each neighborly $d$-sphere with no more than $d+4$ vertices is combinatorially equivalent to a Murai sphere for any $d\geq 1$. |
| title | Neighborly Murai spheres and the Simplicial Steinitz Problem |
| topic | Combinatorics 05E45, 13F55, 52B05, 52B12, 57S12 |
| url | https://arxiv.org/abs/2606.02513 |