Disjoint empty disks supported by a point set

Details Disjoint empty disks supported by a point set Disjoint empty disks supported by a point set

2012-03-02

arxiv.org/abs/1203.0563v1

Mathematics

Combinatorics

18 pages, 8 figures

Scientific paper

For a planar point-set $P$, let D(P) be the minimum number of empty pairwise-disjoint 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.

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