Gronau–Mullin–Rosa orthogonal double cover conjecture for trees

An orthogonal double cover of $K_n$ by copies of a graph $T$ is a collection of isomorphic copies such that every pair of copies shares exactly one edge and every edge of $K_n$ lies in exactly two copies.

Gronau–Mullin–Rosa conjecture. For every $n$-vertex tree $T$ other than the path on $4$ vertices, $K_n$ has an orthogonal double cover by copies of $T$.

The conjecture concerns a design-theoretic covering problem for complete graphs. Its resolution status is not specified in the supplied text.