Reconstructing Nearly Simple Polytopes from their Graph
Abstract
We present a partial description of which polytopes are reconstructible from their graphs. This is an extension of work by Blind and Mani (1987) and Kalai (1988), which showed that simple polytopes can be reconstructed from their graphs. In particular, we introduce a notion of $h$nearly simple and prove that 1nearly simple and 2nearly simple polytopes are reconstructible from their graphs. We also give an example of a 3nearly simple polytope which is not reconstructible from its graph. Furthermore, we give a partial list of polytopes which are reconstructible from their graphs in an entirely nonconstructive way.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.08334
 Bibcode:
 2017arXiv170108334D
 Keywords:

 Mathematics  Combinatorics;
 52Bxx
 EPrint:
 13 pages