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On the kernel of intersecting families

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Abstract

Letℱ be at-wises-intersecting family, i.e.,|F 1 ∩ ... ∩ F t | ≥ s holds for everyt members ofℱ. Then there exists a setY such that|F 1 ∩ ... ∩ F t ∩ Y| ≥ s still holds for everyF 1,...,F t ∈ℱ. Here exponential lower and upper bounds are proven for the possible sizes ofY.

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Authors and Affiliations

  1. Department of Mathematics, Tel Aviv University, 69978, Ramat Aviv, Tel Aviv, Israel

    N. Alon

  2. Mathematical Institute of the Hungarian Academy of Science, P.O.B. 127, 1364, Budapest, Hungary

    Z. Füredi

Authors
  1. N. Alon
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  2. Z. Füredi
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Additional information

This work was done while the authors visited Bell Communication Research, NJ 07960, and AT&T Bell Laboratories, Murray Hill, NJ 07974, USA, respectively.

Research supported in part by Allon Fellowship and by Bat Sheva de Rothschild Foundation.

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Alon, N., Füredi, Z. On the kernel of intersecting families. Graphs and Combinatorics 3, 91–94 (1987). https://doi.org/10.1007/BF01788533

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  • DOI: https://doi.org/10.1007/BF01788533

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