Cliques in Steiner systems |
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Authors: | Andrzej Dudek František Franěk Vojtěch Rödl |
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Institution: | (1) Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA;(2) Department of Computers and Software, McMaster University, Hamilton, ON, Canada |
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Abstract: | A partial Steiner (k,l)-system is a k-uniform hypergraph
with the property that every l-element subset of V is contained in at most one edge of
. In this paper we show that for given k,l and t there exists a partial Steiner (k,l)-system such that whenever an l-element subset from every edge is chosen, the resulting l-uniform hypergraph contains a clique of size t. As the main result of this note, we establish asymptotic lower and upper bounds on the size of such cliques with respect
to the order of Steiner systems.
Research of the second author partially supported by NSERC grant OGP0025112. |
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Keywords: | Ramsey Theorem Steiner Systems |
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