48 citations · 91 across the 23 of their papers we have counts for
3 papers · 1 filter
Regular systems of paths and families of convex sets in convex position
Michael G. Dobbins, Andreas F. Holmsen, Alfredo Hubard
In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of eac…
Convex Equipartitions: The Spicy Chicken Theorem
Roman Karasev, Alfredo Hubard, Boris Aronov
We show that, for any prime power n and any convex body K (i.e., a compact convex set with interior) in Rd, there exists a partition of K into n convex sets with equal volumes and…
The Erdős-Szekeres problem for non-crossing convex sets
Michael G Dobbins, Andreas F Holmsen, Alfredo Hubard
We show an equivalence between a conjecture of Bisztriczky and Fejes T{ó}th about arrangements of planar convex bodies and a conjecture of Goodman and Pollack about point sets in t…