Abstract
Anr-graph is a graph whose basic elements are its vertices and r-tuples. It is proved that to everyl andr there is anε(l, r) so that forn>n 0 everyr-graph ofn vertices andn r−ε(l, r) r-tuples containsr. l verticesx (j), 1≦j≦r, 1≦i≦l, so that all ther-tuples\((x_{i_1 } ^{(1)} ,x_{i_2 } ^{(2)} , \cdots ,x_{i_r } ^{(r)} )\) occur in ther-graph.
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Erdös, P. On extremal problems of graphs and generalized graphs. Israel J. Math. 2, 183–190 (1964). https://doi.org/10.1007/BF02759942
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DOI: https://doi.org/10.1007/BF02759942