论文信息 - An Extremal Problem for Sets with Applications to Graph Theory

An Extremal Problem for Sets with Applications to Graph Theory

Abstract Let X1, …, Xn be n disjoint sets. For 1 ⩽ i ⩽ n and 1 ⩽ j ⩽ h let Aij and Bij be subsets of Xi that satisfy |Aij| ⩽ ri and |Bij| ⩽ si for 1 ⩽ i ⩽ n, 1 ⩽ j ⩽ h, (∪ i A ij ) ∩ (∪ i B ij ) = ⊘ for 1 ⩽ j ⩽ h, (∪ i A ij ) ∩ (∪ i B il ) ≠ ⊘ for 1 ⩽ j h⩽ Π i=1 n r i +s i r i . This result is best possible and has some interesting consequences. Its proof uses multilinear techniques (exterior algebra).

Noga Alon | N. Alon

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