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math.MG2014★ 3 cited
Convex polygons in geometric triangulations
Adrian Dumitrescu, Csaba D. Tóth
We show that the maximum number of convex polygons in a triangulation of points in the plane is . This improves an earlier bound of established by va…
math.MG2014★ 2 cited
On the Total Perimeter of Homothetic Convex Bodies in a Convex Container
Adrian Dumitrescu, Csaba D. Tóth
For two planar convex bodies, and , consider a packing of positive homothets of contained in . We estimate the total perimeter of the bodies in , denoted $…
math.MG2010
New bounds on the average distance from the Fermat-Weber center of a planar convex body
Adrian Dumitrescu, Minghui Jiang, Csaba D. Tóth
The Fermat-Weber center of a planar body is a point in the plane from which the average distance to the points in is minimal. We first show that for any convex body in…