We give a short proof that for any fixed integer k, the maximum number size of a Kk,k-cross free family is linear in the size of the groundset. We also give tight bounds on the maximum size of a Kk-cross free family in the case when F is intersecting or an antichain. Introduction Let F ⊂ 2. Two sets A, B ∈ F cross if 1. A ∩ B 6= ∅. 2. B 6⊂ A and A 6⊂ B. F… (More)
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