83 citations · 542 across the 80 of their papers we have counts for
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Notes about the Caratheodory number
Imre Barany, Roman Karasev
In this paper we give sufficient conditions for a compactum in to have Carathéodory number less than , generalizing an old result of Fenchel. Then we prove the c…
An analogue of Gromov's waist theorem for coloring the cube
Roman Karasev
It is proved that if we partition a -dimensional cube into small cubes and color the small cubes into colors then there exists a monochromatic connected component co…
Turán numbers for -free graphs: topological obstructions and algebraic constructions
Pavle Blagojević, Boris Bukh, Roman Karasev
We show that every hypersurface in contains a large grid, i.e., the set of the form , with . We use this to deduce that the known cons…
Inscribing a regular octahedron into polytopes
Arseniy Akopyan, Roman Karasev
We prove that any simple polytope (and some non-simple polytopes) in admits an inscribed regular octahedron.
Geometric coincidence results from multiplicity of continuous maps
R. N. Karasev
In this paper we study geometric coincidence problems in the spirit of the following problems by B. Grünbaum: How many affine diameters of a convex body in must have…
Kadets type theorems for partitions of a convex body
Arseniy Akopyan, Roman Karasev
For convex partitions of a convex body we prove that we can put a homothetic copy of into each set of the partition so that the sum of homothety coefficients is . In…