---
abstract: |
    There are two possible definitions of the “$s$-disjoint $r$-uniform Kneser hypergraph” of a set system $\T$: The hyperedges are either $r$-sets or $r$-multisets. We point out that Ziegler’s (combinatorial) lower bound on the chromatic number of an $s$-disjoint $r$-uniform Kneser hypergraph only holds if we consider $r$-multisets as hyperedges. We give a new proof of his result and show by example that a similar result does not hold if one considers $r$-sets as hyperedges.

    In case of $r$-sets as hyperedges and $s \geq 2$ the only known lower bounds are obtained from topological invariants of associated simplicial complexes if $r$ is a prime or the power of prime. This is also true for arbitrary $r$-uniform hypergraphs with $r$-sets or $r$-multisets as hyperedges as long as $r$ is a power of a prime.
address: |
    TU Berlin\
    Institut für Mathematik, MA 6-2\
    Straße des 17. Juni 136\
    10623 Berlin
author:
- Carsten Lange
date: 'December 3, 2003'
title: On generalised Kneser colourings
---

[^1]

[^1]: Supported by the DFG Sonderforschungsbereich 288 “Differentialgeometrie und Quantenphysik” in Berlin.
