论文信息 - Improved bounds for Erdős' Matching Conjecture

Improved bounds for Erdős' Matching Conjecture

The main result is the following. Let F be a family of k-subsets of an n-set, containing no s+1 pairwise disjoint edges. Then for n>=(2s+1)k-s one has |F|=<(nk)-(n-sk). This upper bound is the best possible and confirms a conjecture of Erdos dating back to 1965. The proof is surprisingly compact. It applies a generalization of [email protected]'s Intersection Shadow Theorem.

Peter Frankl | P. Frankl

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