Key points are not available for this paper at this time.
Abstract We give a construction of a convex set with cardinality such that contains a convex subset with cardinality . We also consider the following variant of this problem: given a convex set , what is the size of the largest matching such that the set is convex? We prove that there always exists such an with , and that this lower bound is best possible, up to a multiplicative constant.
Bhowmick et al. (Sun,) studied this question.