Weight functions on the Kneser graph and the solution of an intersection problem of Sali

Abstract

LetX, Y be finite sets and suppose thatF is a collection of pairs of sets (F, G),FX,GY satisfying |FF′|≥s, |GG′|≥t and |FF′|+|GG′|≥s+t+1 for all (F, G),F′, G′F. Extending a result of Sali, we determine the maximum ofF.

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References

  1. [1]

    B. Bollobás:Combinatorics, Cambridge Univ. Press, 1986.

  2. [2]

    P. Erdős, C. Ko, R. Rado: Intersection theorems for systems of finite sets,Quart. J. Math. Oxford (2) 12 (1961) 313–320.

    Google Scholar 

  3. [3]

    P. Frankl An Erdős-Ko-Rado theorem for direct products,European J. of Combinatorics, to appear.

  4. [4]

    P. Frankl: On cross-intersecting families,Discrete Math.,108, (1992) 291–295.

    Google Scholar 

  5. [5]

    L. H. Harper: Optimal numberings and isoperimetric problems on graphs,J. Comb. Theory 1 (1966) 385–393.

    Google Scholar 

  6. [6]

    G. O. H. Katona: A theorem of finite sets, in:Theory of Graphs, Proc. Colloq. Tihany, 1966 (Akadémiai Kiadó, 1968) 187–207.

  7. [7]

    G. O. H. Katona: Intersection theorems for systems of finite sets,Acta Math. Acad. Sci. Hung. 15 (1964) 329–337.

    Google Scholar 

  8. [8]

    G. O. H. Katona: Extremal problems for hypergraphs, in: “Combinatorics, Part II” (eds. M. Hall and J. H. van Lint) Math. Centre Tracts 56:13–42, Mathematisch Centre, Amsterdam, 1974.

    Google Scholar 

  9. [9]

    J. B. Kruskal: The number of simplices in a complex, in:Math. Opt. Techniques (Univ. of Calif. Press, 1963), 251–278.

  10. [10]

    L. Lovász: Problem 13.31, in:Combinatorial Problems and Exercises, North Holland, 1979.

  11. [11]

    M. Matsumoto, N. Tokushige: The exact bound in the Erdős-Ko-Rado theorem for cross-intersecting families.J. Comb. Theory A 22 (1989) 90–97.

    Google Scholar 

  12. [12]

    M. Matsumoto, N. Tokushige: A generalization of the Katona theorem for crosst-intersecting families.Graphs and Combinatorics 5 (1989) 159–171.

    Google Scholar 

  13. [13]

    A. Sali: Some intersection theorems.Combinatorica 12 (1992) 351–361.

    Google Scholar 

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Frankl, P., Tokushige, N. Weight functions on the Kneser graph and the solution of an intersection problem of Sali. Combinatorica 13, 413–420 (1993). https://doi.org/10.1007/BF01303513

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AMS subject classification code (1991)

  • 05 A 99