  For a planar point-set $P$, let D(P) be the minimum number of
pairwise-disjoint empty disks such that each point in $P$ lies on the boundary
of some disk. Further define D(n) as the maximum of D(P) over all n-element
point sets. Hosono and Urabe recently conjectured that $D(n)=\lceil n/2
\rceil$. Here we show that $D(n) \geq n/2 + n/236 - O(\sqrt{n})$ and thereby
disprove this conjecture.
