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Cliques in Steiner systems

In: Mathematica Slovaca, vol. 59, no. 1
Wiesław A. Dudek - Vojtěch Rödl - František Franěk

Details:

Year, pages: 2009, 109 - 120
Keywords:
Ramsey theorem, Steiner systems
About article:
A partial Steiner $(k,l)$-system is a $k$-uniform hypergraph $\mathcal{G}$ with the property that every $l$-element subset of $V$ is contained in at most one edge of $\mathcal{G}$. 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.
How to cite:
ISO 690:
Dudek, W., Rödl, V., Franěk, F. 2009. Cliques in Steiner systems. In Mathematica Slovaca, vol. 59, no.1, pp. 109-120. 0139-9918. DOI: https://doi.org/10.2478/s12175-008-0112-1

APA:
Dudek, W., Rödl, V., Franěk, F. (2009). Cliques in Steiner systems. Mathematica Slovaca, 59(1), 109-120. 0139-9918. DOI: https://doi.org/10.2478/s12175-008-0112-1
About edition: