New upper bound on the transversal width of \(T\)(3)-families of discs (Q2572589)

Let \(\mathcal F\) be an arbitrary finite family of disjoint disks of diameter \(1\) in Euclidean plane such that for every three of them there exists a line transversal. The author proves that there exists a transversal strip for \(\mathcal F\) of width less than \(0.65\). He conjectures that this value can be lessened up to \(2\sin (\pi /10) \approx 0.618\).