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• Article
Gerbner, Dániel
Given n points in the plane, a covering path is a polygonal path that visits all the points. If no three points are collinear, every covering path requires at least n/2 segments, and n−1 straight line segments obviously suffice even if the covering pa . . .
• Article
Let S be a set of n points in the unit square [,1]2, one of which is the origin. We construct n pairwise interior-disjoint axis-aligned empty rectangles such that the lower left corner of each rectangle is a point in S, and the rectangles jointly cove . . .
• Article
For points in the unit square , an anchored rectangle packing consists of interior-disjoint axis-aligned empty rectangles such that point is a corner of the rectangle (that is, is anchored at ) for . We show that for every set of points in , there is . . .
• Article
For two planar convex bodies, C and D , consider a packing S of n positive homothets of C contained in D . We estimate the total perimeter of the bodies in S , denoted per(S) , in terms of per(D) and n . When all homothets of C touch the boundary of t . . .
• Article
Löffler, Maarten
We give upper and lower bounds on the maximum and minimum number of geometric configurations of various kinds present (as subgraphs) in a triangulation of $n$ points in the plane. Configurations of interest include \emph{convex polygons}, \emph{star-s . . .
• Article
Schulz, André
We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, nonweighted common geometric graphs drawn on $n$ points in the plane in general position (with no three points collinear): perfect matchings, spannin . . .
• Article