Cutting disjoint disks by straight lines

N. Alon, M. Katchalski, W. R. Pulleyblank

Research output: Contribution to journalArticlepeer-review


For k>0 let f(k) denote the minimum integer f such that, for any family of k pairwise disjoint congruent disks in the plane, there is a direction α such that any line having direction α intersects at most f of the disks. We determine the exact asymptotic behavior of f(k) by proving that there are two positive constants d1, d2 such that d1√k √log k≤f(k)≤d2√k √log k. This result has been motivated by problems dealing with the separation of convex sets by straight lines.

Original languageEnglish
Pages (from-to)239-243
Number of pages5
JournalDiscrete and Computational Geometry
Issue number1
StatePublished - Dec 1989


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