MathDB
perfect matching in square

Source: miklos schweitzer 1992 q10

October 24, 2021
probability and statsgraph theory

Problem Statement

We place n points in the unit square independently, according to a uniform distribution. These points are the vertices of a graph GnG_n. Two points are connected by an edge if the slope of the segment connecting them is nonnegative. Denote by MnM_n the event that the graph GnG_n has a 1-factor. Prove that lim⁡n→∞P(M2n)=1\lim_{n \to \infty} P(M_ {2n}) = 1.
Back to ProblemsView on AoPS