On generalised Kneser colourings

dc.creatorLange, Carsten
dc.date2003-12-02
dc.date.accessioned2026-07-07T05:03:30Z
dc.date.available2026-07-07T05:03:30Z
dc.descriptionThere 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.description7 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0312067
dc.identifierhttp://arxiv.org/abs/math/0312067
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69442
dc.subjectCombinatorics
dc.subjectAlgebraic Topology
dc.subject05C15; 05C65; 05E25; 57M15
dc.titleOn generalised Kneser colourings
dc.typetext

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