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09/12/2023
The maximum size of adjacency-crossing graphs
An adjacency-crossing graph is a graph that can be drawn such that every...
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07/06/2023
Convex Hull Thrackles
A thrackle is a graph drawn in the plane so that every pair of its edges...
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05/23/2023
On the number of tangencies among 1-intersecting curves
Let C be a set of curves in the plane such that no three curves in C int...
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02/15/2022
A new discrete theory of pseudoconvexity
Recently geometric hypergraphs that can be defined by intersections of p...
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11/16/2021
The number of tangencies between two families of curves
We prove that the number of tangencies between the members of two famili...
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03/20/2021
Discrete Helly-type theorems for pseudohalfplanes
We prove discrete Helly-type theorems for pseudohalfplanes, which extend...
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02/23/2021
On the number of hyperedges in the hypergraph of lines and pseudo-discs
Consider the hypergraph whose vertex set is a family of n lines in gener...
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02/13/2020
An almost optimal bound on the number of intersections of two simple polygons
What is the maximum number of intersections of the boundaries of a simpl...
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01/17/2020
On Covering Numbers, Young Diagrams, and the Local Dimension of Posets
We study covering numbers and local covering numbers with respect to dif...
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03/20/2019
Adaptive Majority Problems for Restricted Query Graphs and for Weighted Sets
Suppose that the vertices of a graph G are colored with two colors in an...
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06/11/2018
Plane drawings of the generalized Delaunay-graphs for pseudo-disks
We study general Delaunay-graphs, which are a natural generalizations of...
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06/11/2018
Coloring Delaunay-Edges and their Generalizations
We consider geometric graphs whose vertex set is a finite set of points ...
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11/15/2017