The rainbow matching conjecture $(n,n)\to n-1$

Let $(m,n)\to k$ mean that every $m$ matchings of size $n$ in any graph have a rainbow matching of size $k$. Rainbow matching conjecture.

$$(n,n)\to n-1.$$

The conjecture is stated as a general-graph analogue of a bipartite conjecture, and the source notes that no counterexample is known in general graphs. If true, it would imply the Ryser–Brualdi–Stein conjecture on Latin transversals.