Tolerance for colorful Tverberg partitions

@article{Sarkar2022ToleranceFC,
  title={Tolerance for colorful Tverberg partitions},
  author={Sherry Sarkar and Pablo Sober'on},
  journal={Eur. J. Comb.},
  year={2022},
  volume={103},
  pages={103527}
}

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References

SHOWING 1-10 OF 24 REFERENCES

A Note on the Tolerant Tverberg Theorem

TLDR
This paper gives an asymptotically tight bound for the tolerant Tverberg Theorem when the dimension and the size of the partition are fixed and uses the Erdős–Szekeres theorem to achieve this.

Robust Tverberg and Colourful Carathéodory Results via Random Choice

  • P. Soberón
  • Mathematics
    Combinatorics, Probability and Computing
  • 2017
TLDR
Borders are given 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.

Algorithms for Tolerated Tverberg Partitions

TLDR
Soberon and Strausz proved that there is always a t-tolerated Tverberg partition with ⌈n / (d + 1)(t + 1) ⌉ sets.

Equal coefficients and tolerance in coloured Tverberg partitions

TLDR
It is shown that (k-1)d+1 colour classes are necessary and sufficient if the coefficients in the convex combination in the colourful sets are required to be the same in each class.

Tverberg Partitions as Weak Epsilon-Nets

TLDR
A Tverberg-type theorem is proved using the probabilistic method to find the smallest number of partitions of a set X into r parts needed in order to induce at least one TVerberg partition on every subset of X with at least $\varepsilon |X|$ elements.

Optimal bounds for the colored Tverberg problem

We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Barany et al.

A Colored Version of Tverberg's Theorem

The main result of this paper is that given n red, n white, and n green points in the plane, it is possible to form n vertex-disjoint triangles Delta_{1},...,Delta_{n} in such a way that the