On generalised Kneser colourings
| dc.creator | Lange, Carsten | |
| dc.date | 2003-12-02 | |
| dc.date.accessioned | 2026-07-07T05:03:30Z | |
| dc.date.available | 2026-07-07T05:03:30Z | |
| dc.description | 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. | |
| dc.description | 7 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0312067 | |
| dc.identifier | http://arxiv.org/abs/math/0312067 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69442 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Topology | |
| dc.subject | 05C15; 05C65; 05E25; 57M15 | |
| dc.title | On generalised Kneser colourings | |
| dc.type | text |