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01/18/2023
A Note on the k-colored Crossing Ratio of Dense Geometric Graphs
A geometric graph is a graph whose vertex set is a set of points in gene...
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10/02/2022
No Selection Lemma for Empty Triangles
Let S be a set of n points in general position in the plane. The Second ...
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09/14/2022
Stochastic strategies for patrolling a terrain with a synchronized multi-robot system
A group of cooperative aerial robots can be deployed to efficiently patr...
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07/15/2020
Empty Rainbow Triangles in k-colored Point Sets
Let S be a set of n points in general position in the plane. Suppose tha...
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02/25/2020
A Note on Empty Balanced Tetrahedra in Two colored Point sets in ℝ^3
Let S be a set of n red and n blue points in general position in ℝ^3. Le...
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01/22/2020
Chirotopes of Random Points in Space are Realizable on a Small Integer Grid
We prove that with high probability, a uniform sample of n points in a c...
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08/18/2019
On the 2-colored crossing number
Let D be a straight-line drawing of a graph. The rectilinear 2-colored c...
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07/17/2019
An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants
A drawing of a graph in the plane is pseudolinear if the edges of the d...
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04/24/2019
Counting the Number of Crossings in Geometric Graphs
A geometric graph is a graph whose vertices are points in general positi...
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11/06/2018
On the Number of Order Types in Integer Grids of Small Size
Let {p_1,...,p_n} and {q_1,...,q_n} be two sets of n labeled points in g...
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08/27/2018
Optimal Grid Drawings of Complete Multipartite Graphs and an Integer Variant of the Algebraic Connectivity
How to draw the vertices of a complete multipartite graph G on different...
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04/03/2018
The exact chromatic number of the convex segment disjointness graph
Let P be a set of n points in strictly convex position in the plane. Let...
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02/09/2018