Minimum degree in simplicial complexes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916548386488320 |
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| author | Reiher, Christian Schülke, Bjarne |
| author_facet | Reiher, Christian Schülke, Bjarne |
| contents | Given $d\in\mathbb{N}$, let $α(d)$ be the largest real number such that every abstract simplicial complex $\mathcal{S}$ with $0<\vert\mathcal{S}\vert\leqα(d)\vert V(\mathcal{S})\vert$ has a vertex of degree at most $d$. We extend previous results by Frankl, Frankl and Watanabe, and Piga and Schülke by proving that for all integers $d$ and $m$ with $d\geq m\geq 1$, we have $α(2^d-m)=\frac{2^{d+1}-m}{d+1}$. Similar results were obtained independently by Li, Ma, and Rong. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimum degree in simplicial complexes Reiher, Christian Schülke, Bjarne Combinatorics 05D05, 05E45, 55U10 Given $d\in\mathbb{N}$, let $α(d)$ be the largest real number such that every abstract simplicial complex $\mathcal{S}$ with $0<\vert\mathcal{S}\vert\leqα(d)\vert V(\mathcal{S})\vert$ has a vertex of degree at most $d$. We extend previous results by Frankl, Frankl and Watanabe, and Piga and Schülke by proving that for all integers $d$ and $m$ with $d\geq m\geq 1$, we have $α(2^d-m)=\frac{2^{d+1}-m}{d+1}$. Similar results were obtained independently by Li, Ma, and Rong. |
| title | Minimum degree in simplicial complexes |
| topic | Combinatorics 05D05, 05E45, 55U10 |
| url | https://arxiv.org/abs/2501.01294 |