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- W3095006082 abstract "More than 50 years ago, ErdH os asked the following question: what is the maximum size of a family $mathcal F$ of $k$-element subsets of an $n$-element set if it has no $s+1$ pairwise disjoint sets? This question attracted a lot of attention recently, in particular, due to its connection to various combinatorial, probabilistic and theoretical computer science problems. Improving the previous best bound due to the first author, we prove that $|mathcal F|le {nchoose k}-{n-schoose k}$, provided $nge frac 53sk -frac 23 s$ and $s$ is sufficiently large. We derive several corollaries concerning Dirac thresholds and deviations of sums of random variables. We also obtain several related results." @default.
- W3095006082 created "2020-11-09" @default.
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- W3095006082 date "2018-06-22" @default.
- W3095006082 modified "2023-09-27" @default.
- W3095006082 title "Proof of the ErdH{o}s Matching Conjecture in a New Range" @default.
- W3095006082 hasPublicationYear "2018" @default.
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