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On extremal problems of graphs and generalized graphs. (English) Zbl 0129.39905
An $$r$$-graph $$G$$ consists of a set $$V(G)$$ of elements called vertices of $$G$$ and a set $$E(G)$$ whose elements (called edges of $$G$$) are subsets of $$V(G)$$ with cardinal number $$r$$. (Thus a 2-graph is a graph in the usual sense.) The paper deals with the following problem: given positive integers $$n,r,l$$, estimate the smallest value of $$f$$ such that, for every $$r$$-graph $$G$$ with $$n$$ vertices and $$f$$ edges, $$V(G)$$ has $$r$$ disjoint subsets $$S_1,...,S_r$$ of cardinal number $$l$$ such that $$\{x_1,...,x_r\} \in E(G)$$ whenever $$x_1 \in S_1,...,x_r \in S_r$$. Some related matters are also briefly discussed and some interesting results and unsolved problems in this area are mentioned.

##### MSC:
 05C35 Extremal problems in graph theory
topology
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##### References:
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