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On generalised Kneser colourings | | Carsten Lange
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2 Dec 2003 | | Subject: | Combinatorics; Algebraic Topology MSC-class: 05C15; 05C65; 05E25; 57M15 | math.CO math.AT | | 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. | | Source: | arXiv, math.CO/0312067 | | Services: | Forum | Review | PDF | Favorites | |
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