论文标题
更好地限制了彩虹搭配的大小
A better bound on the size of rainbow matchings
论文作者
论文摘要
Aharoni和Howard猜想，对于积极的整数$ n，k，t $，带有$ n \ ge k $和$ n \ ge t $，如果$ f_1，\ ldots，f_t \ subseteq {[n] \ subseteq {[n] \ select k k} $存在于[t] $中的$ i \中的$ e_i \，因此$ e_1，\ ldots，e_t $是成对的脱节。 Huang，Loh和Sudakov证明了$ t <n/（3k^2）$的猜想。在本文中，我们表明，这种猜想适用于$ t \ le n/（2k）$和$ n $足够大。
Aharoni and Howard conjectured that, for positive integers $n,k,t$ with $n\ge k$ and $n\ge t$, if $F_1,\ldots, F_t\subseteq {[n]\choose k}$ such that $|F_i|>{n\choose k}-{n-t+1\choose k}$ for $i\in [t]$ then there exist $e_i\in F_i$ for $i\in [t]$ such that $e_1,\ldots,e_t$ are pairwise disjoint. Huang, Loh, and Sudakov proved this conjecture for $t<n/(3k^2)$. In this paper, we show that this conjecture holds for $t\le n/(2k)$ and $n$ sufficiently large.
