scholarly journals Tverberg's Theorem at 50: Extensions and Counterexamples

2016 ◽  
Vol 63 (07) ◽  
pp. 732-739 ◽  
Author(s):  
Imre Bárány ◽  
Pavle V. M. Blagojević ◽  
Günter M. Ziegler
Keyword(s):  
Tverberg’S Theorem

scholarly journals Tverberg’s theorem is 50 years old: A survey

2018 ◽  
Vol 55 (4) ◽  
pp. 459-492 ◽  
Author(s):  
Imre Bárány ◽  
Pablo Soberón
Keyword(s):  
Tverberg’S Theorem

Some variations on Tverberg’s theorem

2016 ◽  
Vol 216 (2) ◽  
pp. 957-972 ◽  
Author(s):  
Micha A. Perles ◽  
Moriah Sigron
Keyword(s):  
Tverberg’S Theorem

scholarly journals Roberts-type embeddings and conversion of transversal Tverberg's theorem

2005 ◽  
Vol 196 (11) ◽  
pp. 1585-1603 ◽  
Author(s):  
S A Bogatyi ◽  
V M Valov
Keyword(s):  
Tverberg’S Theorem

An elementary proof of Tverberg’s theorem

2009 ◽  
Vol 161 (3) ◽  
pp. 384-387 ◽  
Author(s):  
M. Yu. Zvagel’skii
Keyword(s):  
Elementary Proof ◽  
Tverberg’S Theorem

scholarly journals Tverberg's theorem with constraints

2008 ◽  
Vol 115 (8) ◽  
pp. 1402-1416 ◽  
Author(s):  
Stephan Hell
Keyword(s):  
Tverberg’S Theorem

scholarly journals Tverberg’s Theorem and Graph Coloring

2013 ◽  
Vol 51 (1) ◽  
pp. 207-220
Author(s):  
Alexander Engström ◽  
Patrik Norén
Keyword(s):  
Graph Coloring ◽  
Tverberg’S Theorem

Robust Tverberg and Colourful Carathéodory Results via Random Choice

2017 ◽  
Vol 27 (3) ◽  
pp. 427-440 ◽  
Author(s):  
PABLO SOBERÓN
Keyword(s):  
Probabilistic Method ◽  
Convex Hulls ◽  
Random Choice ◽  
Tverberg’S Theorem ◽  
Colourful Carathéodory Theorem ◽  
Carathéodory Theorem

We use the probabilistic method to obtain versions of the colourful Carathéodory theorem and Tverberg's theorem with tolerance.In particular, we give bounds for the smallest integer N = N(t,d,r) such that for any N points in ℝd, there is a partition of them into r parts for which the following condition holds: after removing any t points from the set, the convex hulls of what is left in each part intersect.We prove a bound N = rt + O($\sqrt{t}$) for fixed r,d which is polynomial in each parameters. Our bounds extend to colourful versions of Tverberg's theorem, as well as Reay-type variations of this theorem.

Tverberg’s theorem via number fields

1992 ◽  
Vol 79 (2-3) ◽  
pp. 317-320 ◽  
Author(s):  
K. S. Sarkaria
Keyword(s):  
Number Fields ◽  
Tverberg’S Theorem

scholarly journals A Colored Version of Tverberg's Theorem

1992 ◽  
Vol s2-45 (2) ◽  
pp. 314-320 ◽  
Author(s):  
I. Bárány ◽  
D. G. Larman
Keyword(s):  
Tverberg’S Theorem ◽  
Colored Version
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