4 problems

Let $D$ be the complete geometric graph on $n$ points selected uniformly at random from the unit square. For an interval $I\subseteq \mathbb{R}$, color an edge blue when its slope…

Covering-radius conjecture. The expected covering radius satisfies

Limiting distribution conjecture. The scaled hole radii are dependent samples from a distribution whose probability density function converges, as $N\to\infty$, to

Let $K$ be the convex region and let the upper and lower bounds in Theorems 2 and 3 concern the largest empty convex quadrilateral and the largest empty convex polygon, respectivel…