On the graph-connectivity of skeleta of convex polytopes
| dc.creator | Athanasiadis, Christos A. | |
| dc.date | 2008-01-07 | |
| dc.date | 2008-01-10 | |
| dc.date.accessioned | 2026-07-07T08:53:26Z | |
| dc.date.available | 2026-07-07T08:53:26Z | |
| dc.description | Given a $d$-dimensional convex polytope $P$ and nonnegative integer $k$ not exceeding $d-1$, let $G_k (P)$ denote the simple graph on the node set of $k$-dimensional faces of $P$ in which two such faces are adjacent if there exists a $(k+1)$-dimensional face of $P$ which contains them both. The graph $G_k (P)$ is isomorphic to the dual graph of the $(d-k)$-dimensional skeleton of the normal fan of $P$. For fixed values of $k$ and $d$, the largest integer $m$ such that $G_k (P)$ is $m$-vertex-connected for all $d$-dimensional polytopes $P$ is determined. This result generalizes Balinski's theorem on the one-dimensional skeleton of a $d$-dimensional convex polytope. | |
| dc.description | Added Remark 1.2 and reference to the article [Incidence graphs of convex polytopes, J. Combin. Theory 2 (1967), 466-506] by G.T. Sallee | |
| dc.identifier | https://arxiv.org/abs/0801.0939 | |
| dc.identifier | http://arxiv.org/abs/0801.0939 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145624 | |
| dc.subject | Combinatorics | |
| dc.subject | 52B05 | |
| dc.title | On the graph-connectivity of skeleta of convex polytopes | |
| dc.type | text |