Emergent Mind
Matching points with disks with a common intersection
(1902.08427)
Published Feb 22, 2019
in
cs.CG
and
cs.DM
Abstract
We consider matchings with diametral disks between two sets of points R and B. More precisely, for each pair of matched points p in R and q in B, we consider the disk through p and q with the smallest diameter. We prove that for any R and B such that |R|=|B|, there exists a perfect matching such that the diametral disks of the matched point pairs have a common intersection. In fact, our result is stronger, and shows that a maximum weight perfect matching has this property.
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