An extremal problem for sets with applications to graph theory |
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Authors: | Noga Alon |
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Affiliation: | Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 USA |
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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, for 1 ? j ? h, for 1 ? j < l ? h. We prove that . This result is best possible and has some interesting consequences. Its proof uses multilinear techniques (exterior algebra). |
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