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Non-empty cross-3-intersection theorems of subsets

  • Shiquan Wu
Session 6B: Combinatorics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)

Abstract

Maximum families of subsets satisfying some specified conditions are widely studied in combinatorics on set systems. In this paper, an extremal problem on subsets is considered. Let C n k denote the set of all k-subsets of an n- set. Assume AC n a and BC n b , (A B) is called a cross-t-intersecting family if ¦ A ∩ B ¦≥ t for any AA, BB. For t=3, maximum non-empty cross-3-intersecting families of a- and b- subsets are obtained.

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References

  1. 1.
    Anderson,I.,Combinatorics of finite sets, Oxford, 1987Google Scholar
  2. 2.
    Frankl, P. and Tokushige, N., Some best possible inequalities concerning cross-intersecting families, J. Combin. Th. Ser. A61 (1992), 87–97.CrossRefGoogle Scholar
  3. 3.
    Hilton, A. J. W. and Milner, E.C., Some intersection theorems for systems of finite sets, Quart. J. Math. Oxford 18 (2) (1967),369–384.Google Scholar
  4. 4.
    Matsumoto,M., The exact bound in Erdös-Ko-Rado Theorem for cross-intersecting families, J. Comb. Theory A52 (1989), 90–97.CrossRefGoogle Scholar
  5. 5.
    Simpson,J.E., A bipartite Erdös-Ko-Rado Theorem, Discrete Mathematics 113(1993)277–280.CrossRefGoogle Scholar
  6. 6.
    Wu Shiquan, Non-empty cross-2-intersecting families of subsets, Applied Mathematics: A Journal of Chinese Universities, B8(1993)2,176–182.Google Scholar
  7. 7.
    Wu Shiquan, Cross-t-intersection theorems of subsets, Technical Report of the Center of Mathematical Sciences,Zhejiang University,n1(1994).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Shiquan Wu
    • 1
  1. 1.System Engineering and Mathematics DepartmentNational University of Defense Technology ChangshaHunanChina

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