A general 2-part Erdős-Ko-Rado theorem

Katona, Gyula (2017) A general 2-part Erdős-Ko-Rado theorem. OPUSCULA MATHEMATICA, 37 (4). pp. 577-588. ISSN 1232-9274

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Abstract

A two-part extension of the famous Erdo{combining double acute accent}s-Ko-Rado Theorem is proved. The underlying set is partitioned into X1 and X2. Some positive integers ki, ℓi (1 ≤ i ≤ m) are given. We prove that if ℱ is an intersecting family containing members F such that |F ∩ X1| = ki, |F ∩ X2| = ℓi holds for one of the values i (1 ≤ i ≤ m) then |ℱ| cannot exceed the size of the largest subfamily containing one element. © Wydawnictwa AGH, 2017.

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