Matching Ramsey number ($R(r{K}_2,s{K}_2)$)

For $r\ge s\ge 1$, the two-colour Ramsey number for disjoint edge matchings isThus every red-blue colouring of $K_{2r+s-1}$ contains either a red matching of size $r$ or a blue matching of size $s$, and the order is sharp.