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math.CO2026
Crossing numbers of simplicial complexes
Alfredo Hubard, Cheikh Saliou Ndiaye, Oriol Solé-Pi
This paper studies crossing numbers of -dimensional simplicial complexes drawn in or . We clarify and generalize a number of known results and c…
math.CO2026
Uniform Geodesic Drawings of Graphs
Saba Lepsveridze, Oriol Solé-Pi
We study crossing numbers of dense graph drawings whose vertices are uniformly distributed either on the unit sphere or in a compact convex planar domain. We prove a sharp inequali…
math.CO2026
There are many 5-holes
Omar Astudillo-Marbán, Oriol Solé-Pi
Given a set P of points on the plane, a polygon with vertices in P is said to be empty if it contains no element of P in its interior. We show that every set of n points in general…