Abstract.
The still open Hirsch conjecture asserts that Δ(d,n) ≤n-d for all n > d ≥ 2 , where Δ (d,n) denotes the maximum edge-diameter of (convex) d -polytopes with n facets. This paper adds to the list of pairs (d,n) that are known to be H -sharp in the sense that Δ (d,n) ≥ n-d . In particular, it is proved that Δ(d,n)≥ n-d for all n > d ≥ 14 .
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Received November 20, 1996, and in revised form March 21, 1997.
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Holt, F., Klee, V. Many Polytopes Meeting the Conjectured Hirsch Bound. Discrete Comput Geom 20, 1–17 (1998). https://doi.org/10.1007/PL00009372
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DOI: https://doi.org/10.1007/PL00009372