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math.CO2024
Extensions of discrete Helly theorems for boxes
Timothy Edwards, Pablo Soberón
We prove extensions of Halman's discrete Helly theorem for axis-parallel boxes in . Halman's theorem says that, given a set in , if is a finite…
math.CO2023
Tverberg Partition Graphs
Deborah Oliveros, Érika Roldán, Pablo Soberón +1
Given a finite set of points in , Tverberg's theorem guarantees the existence of partitions of this set into parts whose convex hulls intersect. We introduce a graph…
math.CO2023
Colorful and Quantitative Variations of Krasnosselsky's Theorem
Connor Donovan, Danielle Paulson, Pablo Soberón
Krasnosselsky's art gallery theorem gives a combinatorial characterization of star-shaped sets in Euclidean spaces, similar to Helly's characterization of finite families of convex…