Some intersection theorems on two-valued functions



be a family of two-valued functions defined on ann-element set in which each pair of functions in

satisfy a given intersection condition. For certain intersection conditions we determine the maximal value of


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  1. [1]

    R. Ahlswede andG. O. H. Katona, Contributions to the geometry of Hamming spaces,Discrete Math. 17 (1977), 1–22.

    MATH  Article  MathSciNet  Google Scholar 

  2. [2]

    N. G. de Bruijn andP. Erdős, On a combinatorial problem,Proc. Konink Nederland Akad. Wetensch. Amsterdam 51 (1948), 421–423.

    Google Scholar 

  3. [3]

    F. R. K. Chung, R. L. Graham, P. Frankl andJ. Shearer, Some intersection theorems for ordered sets and graphs,to appear.

  4. [4]

    P. Erdős, Chao Ko andR. Rado, Intersection theorems for systems of finite sets,Quart. J. Math. 2 (1961), 313–320.

    Article  Google Scholar 

  5. [5]

    R. L. Graham, M. Simonovits andV. T. Sós, A note on the intersection properties of subsets of integers,J. Comb. Th. (A) 28 (1980), 106–116.

    MATH  Article  Google Scholar 

  6. [6]

    V. Rödl,to appear.

  7. [7]

    M. Simonovits andV. T. Sós, Intersections on structures,Combinatorial Math., Optimal Design and their Applications, Ann. Discrete Math.6 (1980), 301–314.

    MATH  Google Scholar 

  8. [8]

    M. Simonovits andV. T. Sós, Intersection theorems for subsets of integers,European Journal of Comb. 2 (1981), 363–372.

    MATH  Google Scholar 

  9. [9]

    M. Simonovits andV. T. Sós, Graph intersection theorems,Proc. Colloq. Combinatorics and Graph Theory, Orsay, Paris, 1976, 389–391.

    Google Scholar 

  10. [10]

    M. Simonovits andV. T. Sós, Intersection theorems for graphs II,Coll. Math. Soc. J. Bolyai 18,Combinatorics, Keszthely, Hungary (1976), 1017–1029.

    Google Scholar 

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Faudree, R.J., Schelp, R.H. & Sós, V.T. Some intersection theorems on two-valued functions. Combinatorica 6, 327–333 (1986).

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AMS subject classification (1980)

  • 05 C 35