Covering Points with Disjoint Unit Disks.
Greg Aloupis, Robert Aubrey Hearn, Hirokazu Iwasawa, Ryuhei Uehara · 2012
We consider the following problem. How many points must be placed in the plane so that no collection of disjoint unit disks can cover them? The answer, k, is already known to satisfy 11 ≤ k ≤ 53. Here, we improve the lower bound to 13 and the upper bound to 50. We also provide a set of 45 points that apparently cannot be covered, although this has been determined via computer search.