Katona’s Intersection Theorem: Four Proofs

It is known from a previous paper [3] that Katona’s Intersection Theorem follows from the Complete Intersection Theorem by Ahlswede and Khachatrian via a Comparison Lemma. It also has been proved directly in [3] by the pushing–pulling method of that paper. Here we add a third proof via a new (k,k+1)-shifting technique, whose impact will be exploared elsewhere. The fourth and last of our proofs is a gift from heaven for Gyula’s birthday.

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Correspondence to R. Ahlswede.

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Presented on the Conference on Hypergraphs held in Budapest June 7–9, 2001 in Honour of Gyula Katona on the occasion of his 60th Birthday.

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Ahlswede, R., Khachatrian, L.H. Katona’s Intersection Theorem: Four Proofs. Combinatorica 25, 105–110 (2004). https://doi.org/10.1007/s00493-005-0008-4

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Mathematics Subject Classification (2000):

  • 05C35
  • 05C65
  • 05D05