Let A be a family of convex sets in R d . A line transversal to A is a line which intersects every member of A. More generally, a k-tranversal to A is an ane subspace of dimension k which intersects every member of A.

New upper bound on the transversal width of T (3)-families of discs. (English summary) Discrete Comput. Geom. 34 (2005), no. 3, 463–474. Given a finite set S of disjoint copies of the closed unit disc in the plane, for any three elements of S there is a line with non-empty intersection with all three. The problem is to find a strip with small width which has non-empty intersection with every member of S. It was proved by J. Eckhoff [Arch. Math. (Basel) 24 (1973), 195–202; MR0320893 (47 #9426)] that there exists a strip of width 1 intersecting all members of S. The main result of the present paper is to show that there exists a strip of width < 0.65 intersecting all members of S. It is conjectured that < 0.65 can be replaced by ≤ 2 sin (π/10) = 0.618....