# A colored Tverberg type theorem for unavoidable complexes

## TL;DR

This paper proves a new colored Tverberg theorem for rainbow-unavoidable complexes, combining previous theorems using discrete Morse theory to advance understanding in topological combinatorics.

## Contribution

It introduces a novel colored Tverberg theorem for rainbow-unavoidable complexes, merging two existing theorems with a new proof approach.

## Key findings

- Established a colored Tverberg theorem for rainbow-unavoidable complexes
- Unified two previous theorems in topological combinatorics
- Applied discrete Morse theory as a key proof technique

## Abstract

The main result of this paper is a "colored Tverberg theorem for rainbow-unavoidable complexes". This theorem may be considered as a merging of two theorems: "Tverberg theorem for collectively unavoidable complexes" and "balanced colored Tverberg theorem". The main tool for the proof is discrete Morse theory.