Randomized construction of complexes with large diameter
We consider the question of the largest possible combinatorial diameter among pure dimensional and strongly connected (d-1)-dimensional simplicial complexes on n vertices, denoted H_s(n, d). Using a probabilistic construction we give a new lower bound on H_s(n, d) that is within an O(d^2) factor of the upper bound. This improves on the previously best known lower bound which was within a factor of e^varTheta (d) of the upper bound. We also make a similar improvement in the case of pseudomanifolds.
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Published in: Discrete and Computational Geometry, 10.1007/s00454-020-00248-2, SpringerNature