Extension complexity of polytopes with few vertices or facets
نویسنده
چکیده
We study the extension complexity of polytopes with few vertices or facets. On the one hand, we provide a complete classification of d-polytopes with at most d + 4 vertices according to their extension complexity: Out of the super-exponentially many d-polytopes with d+4 vertices, all have extension complexity d+ 4 except for some families of size θ(d). On the other hand, we show that generic realizations of simplicial/simple d-polytopes with d+ 1 +α vertices/facets have extension complexity at least 2 √ d(d+ α) − d + 1, which shows that for all d > (α−1 2 ) there are d-polytopes with d + 1 + α vertices or facets and extension complexity d+ 1 + α.
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 30 شماره
صفحات -
تاریخ انتشار 2016