Reconstructing a Simple Polytope from its Graph
| dc.creator | Kaibel, Volker | |
| dc.date | 2002-02-12 | |
| dc.date.accessioned | 2026-07-07T04:46:24Z | |
| dc.date.available | 2026-07-07T04:46:24Z | |
| dc.description | Blind and Mani (1987) proved that the entire combinatorial structure (the vertex-facet incidences) of a simple convex polytope is determined by its abstract graph. Their proof is not constructive. Kalai (1988) found a short, elegant, and algorithmic proof of that result. However, his algorithm has always exponential running time. We show that the problem to reconstruct the vertex-facet incidences of a simple polytope P from its graph can be formulated as a combinatorial optimization problem that is strongly dual to the problem of finding an abstract objective function on P (i.e., a shelling order of the facets of the dual polytope of P). Thereby, we derive polynomial certificates for both the vertex-facet incidences as well as for the abstract objective functions in terms of the graph of P. The paper is a variation on joint work with Michael Joswig and Friederike Koerner (2001). | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0202103 | |
| dc.identifier | http://arxiv.org/abs/math/0202103 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63315 | |
| dc.subject | Combinatorics | |
| dc.subject | Metric Geometry | |
| dc.subject | 52B11 (Primary) 52B05, 52B22 (Secondary) | |
| dc.title | Reconstructing a Simple Polytope from its Graph | |
| dc.type | text |