Mathematical and Physical Journal
for High Schools
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Problem A. 504. (March 2010)

A. 504. Prove that for arbitrary integers 0<r<k<t there exists a positive integer N(r,k,t) which satisfies the following property: whenever G is an r-uniform hypergraph with at least N(r,k,t) vertices such that there is at least one hyperedge on any k vertices, then G contains a complete subgraph with t vertices. (A hypergraph is a graph whose edges are arbitrary subsets of the vertices. The graph is called r-uniform if all edges contain exactly r vertices. An r-uniform hypergraph is complete if any r of its vertices form an edge.)

(5 pont)

Deadline expired on April 12, 2010.


7 students sent a solution.
5 points:Backhausz Tibor, Bodor Bertalan, Éles András, Frankl Nóra, Nagy 235 János, Weisz Ágoston.
4 points:Nagy 648 Donát.

Problems in Mathematics of KöMaL, March 2010