• Corpus ID: 18659689

A PROBLEM ON INDEPENDENT r-TUPLES

@inproceedings{Erdos1965APO,
  title={A PROBLEM ON INDEPENDENT r-TUPLES},
  author={Paul L. Erdos},
  year={1965}
}
then G(n ; l) contains k independent edges . It is easy to see that the above result is best possible since the complete graph of 2k-1 vertices and the graph of vertices x1, . . ., xk-1 ; Yl, • • •, Yn-k+l and edges (x1 , xj), 1I ; (x1 , y), 1 i :!-< k 1, 1-yj :!5 n k + 1 clearly does not contain k independent edges . By an r-graph o(r) we shall mean a graph whose basic elements are its vertices and r-tuples ; for r = 2 we obtain the ordinary graphs . G (r) (n ; m) will denote an r-graph of n… 
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References

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INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
2. Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the set
RADO, Intersection theorems for systems of finite sets, Quarterly
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