The Cycle Method and Its Limits

  • Gyula O. H. Katona


A powerful tool of extremal set theory, the cycle method is surveyed in the paper. It works, however only when the non-emptyness of the pairwise intersections of the members of the family is assumed. If these intersections have to be at least 2, the method fails: the celebrated Complete Intersection Theorem by Ahlswede and Khachatrian cannot be proved by this method. We show the reasons and some attempts to overcome the difficulties.


Convex Hull Cyclic Permutation Steiner System Cycle Method Profile Vector 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Gyula O. H. Katona
    • 1
  1. 1.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary

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