On a Turán type problem of Erdös

Combinatorica volume 11, pages75–79(1991)Cite this article

Abstract

Let Lk be the graph formed by the lowest three levels of the Boolean lattice B k , i.e.,V(Lk)={0, 1,...,k, 12, 13,..., (k−1)k} and 0is connected toi for all 1≤i≤k, andij is connected toi andj (1≤i<j≤k).

It is proved that if a graph G overn vertices has at leastk 3/2 n 3/2 edges, then it contains a copy of Lk.

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References

  1. [1]

    B. Bollobás,Extremal Graph Theory, Academic Press, London-New York, 1978.

    Google Scholar 

  2. [2]

    W. G. Brown, On graphs that do not contain a Thomsen graph,Canad. Math. Bull. 9 (1966), 281–289.

    Google Scholar 

  3. [3]

    D. de Caen, Extension of a theorem of Moon and Moser on complete hypergraphs,Ars Combinatoria,16 (1983), 5–10.

    Google Scholar 

  4. [4]

    P. Erdős, On some extremal problems in graph theory,Israel J. Math. 3 (1965), 113–116.

    Google Scholar 

  5. [5]

    P. Erdős, Some recent results on extremal problems in graph theory,Theory of Graphs (Internat. Sympos, Rome, 1966), Gordon and Breach, New York, 1967, 117–130.

    Google Scholar 

  6. [6]

    P. Erdős, Extremal problems on graphs and hypergraphs,in Hypergraph Seminar (Proc. First Working Sem., Ohio State Univ., Colubmus, Ohio, 1972)Lecture Notes in Math. 411, Springer, Berlin, 1974. pp. 75–84.

    Google Scholar 

  7. [7]

    P. Erdős, Problems and results on finite and infinite combinatorial analysis,in Infinite and Finite Sets (Proc. Conf. Keszthely, Hungary, 1973.)Proc. Colloq. Math. Soc. J. Bolyai 10 Bolyai-North-Holland, 1975. pp. 403–424.

  8. [8]

    P. Erdős, A. Rényi andV. T. Sós, On a problem of graph theory,Studia Sci. Math. Hungar. 1 (1966), 215–235.

    Google Scholar 

  9. [9]

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

    Google Scholar 

  10. [10]

    P. Erdős andM. Simonovits, Cube-supersaturated graphs and related problems,Progress in graph Theory (Waterloo, Ont. 1982), 203–218. Academic Press, Toronto, Ont., 1984.

    Google Scholar 

  11. [11]

    P. Erdős andA. H. Stone, On the structure of linear graphs,Bull. Amer. Math. Soc. 52 (1946), 1087–1091.

    Google Scholar 

  12. [12]

    Z. Füredi, Quadrilateral-free graphs with maximum number of edges,to appear

  13. [13]

    T. Kővári, V. T. Sós, andP. Turán, On a problem of K. Zarankiewicz,Colloquium Math. 3 (1954), 50–57.

    Google Scholar 

  14. [14]

    M. Simonovits, Extremal graph problems, degenerate extremal problems, and supersaturated graphs,Progress in graph Theory (Waterloo, Ont. 1982), 419–437. Academic Press, Toronto, Ont., 1984.

    Google Scholar 

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Affiliations

  1. Mathematical Institute of the, Hungarian Academy of Sciences, P. O. B. 127, 1364, Budapest, Hungary

    Zoltán Füredi

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  1. Zoltán Füredi
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Research supported in part by the Hungarian National Science Foundation under Grant No. 1812

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Füredi, Z. On a Turán type problem of Erdös. Combinatorica 11, 75–79 (1991). https://doi.org/10.1007/BF01375476

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AMS subject classification (1980)

  • 05 C 35
  • 05 C 65