On an open problem of Paul Turán concerning 3-graphs

  • W. G. Brown


The third of Paul Turán’s 1961 list of Research Problems [4] reads:

“If 2 ≦ l < k < n, then what is the minimal number μ of combinations C 1,C 2,..., C μ taken l at a time out of 1, 2,..., n with the property that each combination taken k at a time out of 1, 2,..., n contains at least one C j ? (For l = 2 the question is settled with exhibiting the only minimal C-system in my paper “Egy gráfelméleti szélsőérték-feladatról”, Mat. és Fiz. Lapok (1941) 436–451, in Hungarian with German abstract.)”


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  1. [1]
    G. Ringel, Extremal Problems in the Theory of Graphs, Theory of Graphs and its Applications (Proc. Sympos. Smolenice, 1963), pp. 85–90. Publ. House Czechoslovak Acad. Sci., Prague, 1964.Google Scholar
  2. [2]
    M. Simonovits, Extremal graph problems with conditions, Combinatorial Theory and its Applications III, Colloquia Math. Soc. J. Bolyai, 4, North-Holland Publishing Co., Amsterdam-London, 1970, 999–1012.Google Scholar
  3. [3]
    V. T. Sós, P. Erdős and W. G. Brown, On the existence of triangulated spheres in 3-graphs, and related problems, Period. Math. Hung., 3 (1973), 221–228.CrossRefGoogle Scholar
  4. [4]
    P. Turán, Research Problems, Magy. Tud. Akad. Mat. Kut. Int. Közl., 6 (1961), 417–423.Google Scholar

Copyright information

© Springer Basel AG 1983

Authors and Affiliations

  • W. G. Brown
    • 1
  1. 1.McGill UniversityMontréalCanada

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