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The maximum number of digons formed by pairwise crossing pseudocircles
Eyal Ackerman, Gábor Damásdi, Balázs Keszegh +2
In 1972, Branko Grünbaum conjectured that any arrangement of pairwise crossing pseudocircles in the plane can have at most digons (regions enclosed by exactly two pseu…
On tangencies among planar curves with an application to coloring L-shapes
Eyal Ackerman, Balázs Keszegh, Dömötör Pálvölgyi
We prove that there are tangencies among any set of red and blue planar curves in which every pair of curves intersects at most once and no two curves of the same color…
Coloring hypergraphs defined by stabbed pseudo-disks and ABAB-free hypergraphs
Eyal Ackerman, Balázs Keszegh, Dömötör Pálvölgyi
What is the minimum number of colors that always suffice to color every planar set of points such that any disk that contains enough points contains two points of different colors?…
Coloring Delaunay-Edges and their Generalizations
Eyal Ackerman, Balázs Keszegh, Dömötör Pálvölgyi
We consider geometric hypergraphs whose vertex set is a finite set of points (e.g., in the plane), and whose hyperedges are the intersections of this set with a family of geometric…