Abstract
Let \({\cal F}\) be a family of convex figures in the plane. We say that \({\cal F}\) has property T if there exists a line intersecting every member of \({\cal F}\). Also, the family \({\cal F}\) has property T(k) if every k-membered subfamily of \({\cal F}\) has property T. Let B be the unit disc centered at the origin. In this paper we prove that if a finite family \({\cal F}=\{x_i+B\colon \ i\in I\}\) of translates of B has property T(4) then the family \({\cal F'}=\{x_i+\lambda B\colon \ i\in I\}\), where \(\lambda= ({1+\sqrt{5}})/{2}\), has property T. We also give some results concerning families of translates of the unit disc which has either property T(3) or property T(5).
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Castro, J. Line Transversals to Translates of Unit Discs. Discrete Comput Geom 37, 409–417 (2007). https://doi.org/10.1007/s00454-006-1281-8
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DOI: https://doi.org/10.1007/s00454-006-1281-8