Sách A tight lower bound for convexly independent subsets of the Minkowski sums of planar point sets ∗

Abstract
Recently, Eisenbrand, Pach, Rothvoß, and Sopher studied the function M(m, n),
which is the largest cardinality of a convexly independent subset of the Minkowski
sum of some planar point sets P and Q with |P | = m and |Q| = n. They proved
that M(m, n) = O(m
2/3
n
2/3
+m+n), and asked whether a superlinear lower bound
exists for M(n, n). In this note, we show that their upper bound is the best possible
apart from constant factors.