Combinatorics of `unavoidable complexes

Combinatorics of `unavoidable complexes

The partition number $\pi(K)$ of a simplicial complex $K\subset 2^{[n]}$ is the minimum integer $\nu$ such that for each partition $A_1\uplus\ldots\uplus A_\nu = [n]$ of $[n]$ at least one of the sets $A_i$ is in $K$. A complex $K$ is $r$-unavoidable if $\pi(K)\leq r$. Motivated by the problems of T...

Full description

Saved in:
Bibliographic Details
Main Authors: Milutinović, Marija Jelić, Jojić, Duško, Timotijević, Marinko, Vrećica, Siniša T, Živaljević, Rade T
Format: Journal Article
Language:English
Published: 30-12-2016
Subjects:
Mathematics - Combinatorics
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The partition number $\pi(K)$ of a simplicial complex $K\subset 2^{[n]}$ is the minimum integer $\nu$ such that for each partition $A_1\uplus\ldots\uplus A_\nu = [n]$ of $[n]$ at least one of the sets $A_i$ is in $K$. A complex $K$ is $r$-unavoidable if $\pi(K)\leq r$. Motivated by the problems of Tverberg-Van Kampen-Flores type, and inspired by the `constraint method' of Blagojevi\'{c}, Frick, and Ziegler, arXiv:1401.0690 [math.CO], we study the combinatorics of $r$-unavoidable complexes.
DOI:10.48550/arxiv.1612.09487