48 citations · 165 across the 65 of their papers we have counts for
7 papers · 1 filter
Approximating the rectilinear crossing number
Jacob Fox, Janos Pach, Andrew Suk
A straight-line drawing of a graph is a mapping which assigns to each vertex a point in the plane and to each edge a straight-line segment connecting the corresponding two poin…
Weight Balancing on Boundaries
Luis Barba, Otfried Cheong, Michael Gene Dobbins +8
Given a polygonal region containing a target point (which we assume is the origin), it is not hard to see that there are two points on the perimeter that are antipodal, that is, wh…
A lower bound on opaque sets
Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi +1
It is proved that the total length of any set of countably many rectifiable curves, whose union meets all straight lines that intersect the unit square U, is at least 2.00002. This…
The number of distinct distances from a vertex of a convex polygon
Gabriel Nivasch, János Pach, Rom Pinchasi +1
Erdős conjectured in 1946 that every n-point set P in convex position in the plane contains a point that determines at least floor(n/2) distinct distances to the other points of P.…
A note on coloring line arrangements
Eyal Ackerman, Rom Pinchasi
We show that the lines of every arrangement of lines in the plane can be colored with colors such that no face of the arrangement is monochromatic. This i…
The visible perimeter of an arrangement of disks
Gabriel Nivasch, János Pach, Gábor Tardos
Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter---the total length of all pieces of their b…