This investigation reveals divergence in discrepancies in hypergraphs as vertex and edge counts equalize, suggesting better estimates.
We investigate the sharpness of general discrepancy estimates for hypergraphs, including weighted ones. We show that in the case when the number of vertices is equal to the number of edges, the average and minimal discrepancies may asymptotically diverge. Moreover, we find a class of vertex-weighted hypergraphs for which the discrepancy estimate is asymptotically order-optimal (as the number of vertices tends to infinity).
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Astashkin et al. (2025) studied this question.
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