Abstract
The n-dimensional random twisted hypercube Gn is constructed recursively by taking two instances of Gn−1, with any joint distribution, and adding a random perfect matching between their vertex sets. Benjamini, Dikstein, Gross, and Zhukovskii showed that its diameter is O(nlogloglogn/loglogn) with high probability and at least (n−1)/log2n. We improve their upper bound by showing that diam(Gn)=(1+o(1))nlog2n with high probability.
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