| Autor: |
Hibi, Takayuki, Mori, Aki |
| Rok vydání: |
2023 |
| Předmět: |
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| DOI: |
10.48550/arxiv.2307.08447 |
| Popis: |
Let ${\rm sk}({\mathcal P})$ denote the $1$-skeleton of an convex polytope ${\mathcal P}$. Let $C$ be a clique (=complete subgraph) of ${\rm sk}({\mathcal P})$ and ${\rm conv}(C)$ the convex hull of the vertices of ${\mathcal P}$ belonging to $C$. In general, ${\rm conv}(C)$ may not be a face of ${\mathcal P}$. It will be proved that ${\rm conv}(C)$ is a face of ${\mathcal P}$ if ${\mathcal P}$ is either the order polytope ${\mathcal O}(P)$ of a finite partially ordered set $P$ or the stable set polytope ${\rm Stab}(G)$ of a finite simple graph $G$. In other words, when ${\mathcal P}$ is either ${\mathcal O}(P)$ or ${\rm Stab}(G)$, the simplicial complex consisting of simplices which are faces of ${\mathcal P}$ is the clique complex of ${\rm sk}({\mathcal P})$. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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