volume 28, issue 1, P29-44 2002
DOI: 10.1007/s00454-001-0085-0
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## Abstract: Abstract. The combinatorial structure of a d-dimensional simple convex polytope -as given, for example, by the set of the (d−1)-regular subgraphs of the facets -can be reconstructed from its abstract graph. However, no polynomial/efficient algorithm is known for this task, although a polynomially checkable certificate for the correct reconstruction exists.A much stronger certificate would be given by the following characterization of the facet subgraphs, conjectured by M. Perles: "The facet subgraphs of a sim…

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