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Asymptotic solution for a new class of forbiddenr-graphs

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Abstract

We consider the problem of finding ex (n; G), defined as the maximal number of edges anr-graph onn vertices can have that contains no subgraph isomorphic toG. We construct certainr-graphsG for which we find the coefficientτ(G) of the asymptotic expansion ex(n;G)==\((\tau (G) + o(1))\left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)\) asn→∞.

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References

  1. B. Bollobás, Tree-graphs without two triples whose symmetric difference is contained in a third,Discrete Math.,8 (1974), 21–24.

    Google Scholar 

  2. W. G. Brown andM. Simonovits, Digraph extremal problems, hypergraph extremal problems, and the densities of graph structures,Discrete Math.,48 (1984), 147–162.

    Google Scholar 

  3. D.de Caen, On Turan's hypergraph problem,Ph. D. Thesis, Univ. Toronto, 1982.

  4. P. Erdős andT. Gallai, On maximal paths and circuits of graphs,Acta Math. Hung.,10 (1959), 337–356.

    Google Scholar 

  5. P.Erdős, Extremal problems in graph theory, In:Theory of graphs and its applications, Proc. Sympos. Smolenice, Prague, 1964, 29–36.

  6. P. Erdős andM. Simonovits, A limit theorem in graph theory,Studia Math. Hung.,1 (1966), 51–57.

    Google Scholar 

  7. P. Frankl andV. Rödl, Hypergraphs do not jump,Combinatorica,4 (1984), 149–159.

    Google Scholar 

  8. G. Katona, T. Nemetz andM. Simonovits, On a graph problem of Turan,Mat. Lapok,XV. 1–3 (1964), 228–238, (in Hungarian).

    Google Scholar 

  9. T. S. Motzkin andE. G. Strauss, Maxima of graphs and a new proof of a theorem of Turan,Canadian J. of Math.,17 (1965), 533–540.

    Google Scholar 

  10. A. F. Sidorenko, The method of quadratic forms and Turán's combinatorial problem,Moscow. Univ. Math. Bull.,37 (1982), 3–6.

    Google Scholar 

  11. A. F. Sidorenko, On the maximal number of edges in a uniform hypergraph without forbidden subgraphs,Math. Notes,41 (1987), 247–259.

    Google Scholar 

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  1. Leninskiy prospect d. 52, kv. 409, 117 333, Moscow, U.S.S.R.

    A. F. Sidorenko

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  1. A. F. Sidorenko
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Sidorenko, A.F. Asymptotic solution for a new class of forbiddenr-graphs. Combinatorica 9, 207–215 (1989). https://doi.org/10.1007/BF02124681

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  • DOI: https://doi.org/10.1007/BF02124681

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