8 citations · 29 across the 18 of their papers we have counts for
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math.MG2013★ 6 cited
A point in a -Polytope is the barycenter of points in its -faces
Michael Gene Dobbins
Using equivariant topology, we prove that it is always possible to find points in the -dimensional faces of a -dimensional convex polytope so that their center of ma…
math.MG2013
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…
math.CO2013★ 4 cited
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…