Mathematics – Combinatorics
Scientific paper
2003-12-02
Mathematics
Combinatorics
7 pages, 1 figure
Scientific paper
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.
No associations
LandOfFree
On generalised Kneser colourings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On generalised Kneser colourings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On generalised Kneser colourings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-187944