Reconstructing Nearly Simple Polytopes from their Graph

Preprint English OPEN
Doolittle, Joseph;
  • Subject: Mathematics - Combinatorics | 52Bxx
    arxiv: Mathematics::Metric Geometry | Mathematics::Combinatorics

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 no... View more
  • References (6)

    [1] Roswitha Blind and Peter Mani-Levitska. Puzzles and polytope isomorphisms. In Computer aided geometric reasoning, Vol. I, II (Sophia-Antipolis, 1987), pages 255-274. INRIA, Rocquencourt, 1987.

    [2] Eric J. Friedman. Finding a simple polytope from its graph in polynomial time. Discrete & Computational Geometry, 41(2):249-256, 2009.

    [3] Haase and Ziegler. Examples and counterexamples for the perles conjecture. Discrete Comput. Geom., 28(1):29-44, July 2002.

    [4] Michael Joswig, Volker Kaibel, and Friederike K¨orner. On thek-systems of a simple polytope. Israel Journal of Mathematics, 129(1):109-117, 2002.

    [5] Gil Kalai. A simple way to tell a simple polytope from its graph. J. Combin. Theory Ser. A, 49(2):381-383, 1988.

    [6] Hiroyuki Miyata, Sonoko Moriyama, and Komei Fukuda. Classification of Oriented Matroids, 2016 (accessed December 21, 2016).

  • Metrics
Share - Bookmark