An
m-transversal to a family of convex sets in the plane is an
m-point set which intersects every members of the family. One of Grübaum’s conjectures says that a planar family of translates
of a convex compact set has a 3-transversal provided that any two of its members intersect. Recently the conjecture has been
proved affirmatively (see [4]). In the present paper we provide a different and straightforward proof for the conjecture for
the family of translates of a closed trapezoid in the plane and give several concrete 3-transversals.
AMS Mathematics Subject Classification 52C15
Key words and phrases Point transversal - convex set - translate
This research was supported by NSFH (199174) and Science Foundation of Hebei Normal University.
Liping Yuan received her BSc and MSc and Ph. D. from the Hebei Normal University under the direction of Prof. Ren Ding. Her research
interests focus on discrete geometry, convex geometry and combinatorial geometry.
Ren Ding is a professor of mathematics, supervising Ph. D. programs at Hebei Normal University. His research interests focus on discrete
geometry, convex geometry and combinatorial geometry.