Extremal Problem for Matchings and Rainbow Matchings on Direct Products

Jian Wang, Jie You

Let $n_1,\dots ,n_{\ell },k_1,\dots ,k_{\ell }$ be integers and let $V_1,\dots ,V_{\ell }$ be disjoint sets with $|V_i|=n_i$ for $i=1,\dots ,\ell$. Define ${\bigsqcup }_{i=1}^{\ell }\left(\genfrac{}{}{0ex}{}{V_i}{k_i}\right)$ a…