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Extension of a theorem of Moon and Moser on complete subgraphs. (English) Zbl 0532.05037
Let G denote a hypergraph with n vertices whose edges are k-tuples of vertices. Let $$N_ h$$ denote the number of complete h-graphs with h vertices and $$\left( \begin{matrix} h\\ k\end{matrix} \right)$$ edges contained in G. The author extends an argument of J. W. Moon and L. Moser [Publ. Math. Inst. Hungar. Acad. Sci., Ser. A 7, 283-286 (1962; Zbl 0114.012)] to give a lower bound for $$N_{h+1}$$ in terms of $$N_ h$$ and $$N_{h-1}$$. From this he deduces an improved general upper bound on the number of edges possible in G if it is to contain no complete h-graph.
Reviewer: J.W.Moon

##### MSC:
 05C35 Extremal problems in graph theory 05C65 Hypergraphs
##### Keywords:
Turan number; complete graphs