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Erdős Matching Conjecture for almost perfect matchings
Published 3 Jun 2022 in math.CO and cs.DM | (2206.01526v2)
Abstract: In 1965 Erd\H{o}s asked, what is the largest size of a family of $k$-element subsets of an $n$-element set that does not have a matching of size $s+1$? In this note, we improve upon a recent result of Frankl and resolve this problem for $s>101k{3}$ and $(s+1)k\le n<(s+1)(k+\frac{1}{100k})$.
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