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# Digraph extremal problems, hypergraph extremal problems, and the densities of graph structures

@article{Brown1984DigraphEP, title={Digraph extremal problems, hypergraph extremal problems, and the densities of graph structures}, author={W. G. Brown and Mikl{\'o}s Simonovits}, journal={Discrete Mathematics}, year={1984}, volume={48}, pages={147-162} }

- Published 1984 in Discrete Mathematics
DOI:10.1016/0012-365X(84)90178-X

We consider extremal problems 'of Tur~ type' for r-uniform ordered hypergraphs, where multiple oriented edges are permitted up to multiplicity q. With any such '(r, q)-graph' G" we associate an r-linear form whose maximum over the standard (n 1)-simplex in R" is called the (graph-) density g(G ") of G". If ex(n, L) is the maximum number of oriented hyperedges in an n-vertex (r, q)-graph not containing a member of L, l i r n ~ ex(n, L)/nr is called the examnal density of L. Motivated, in part… CONTINUE READING

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