Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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POINT TRANSVERSALS TO TRANSLATES OF A TRAPEZOID

  • Yuan, Li-Ping (Department of Mathematics, Hebei Normal University) ;
  • Ding, Ren (Department of Mathematics, Hebei Normal University)
  • Published : 2004.05.01

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Abstract

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 Grubaum'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.

Keywords

References

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