Ryser–Brualdi–Stein Latin-square transversal conjecture

A Latin square of order $n$ is an $n\times n$ array in which each symbol occurs exactly once in every row and column. A partial transversal is a set of cells with no two in the same row, column, or symbol; a full transversal has $n$ cells. Ryser–Brualdi–Stein conjecture. Every Latin square of order $n$ has a partial transversal with at least $n-1$ cells, and, if $n$ is odd, a full transversal. The source presents this as the principal general transversal conjecture and does not give a resolution.