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A Quadratic Lower Bound for the Shield Number of the Stable Marriage Problem: Rearrangement, Extremal Construction, and Biclique Realizability
We study the Shield number of the stable marriage problem, defined as the minimum, over all preference profiles of size n, of the maximum number of blocking pairs attainable by a complete matching. We establish the universal quadratic lower bound $σ(n) \ge \lceil n(n-2)/6 \rceil$ using a rearrangeme
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