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Induced matchings in point-tube incidence graphs

Dmitrii Zakharov (MIT)
Thu, May 23 2024, 3:00pm
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Consider the incidence graph between the points of the unit square and the set of δ x 1 tubes for some δ > 0. What is the size n = n(δ) of the largest induced matching in this graph? We use ideas from projection theory to study this problem and show a non-trivial upper bound on n(δ). As a consequence, we derive a new upper bound on the Heilbronn's triangle problem: any set of n points in the unit square contains a triangle of area at most n^{-7/6}. Joint work with Alex Cohen and Cosmin Pohoata.