Kotzig's Conjecture

For any tree $T$ with $n$ edges, the complete graph $K_{2n+1}$ decomposes into $2n+1$ edge-disjoint copies of $T$ via cyclic shifts of a single embedding.

The $2n+1$ copies are $f_0, f_1, \dots, f_{2n}$ where $f_i(v) = f_0(v) + i$ for all vertices $v$ , each copy is obtained by adding $i \pmod{2n+1}$ to every vertex of the base copy. This is strictly stronger than RingelConjecture.ringel_conjecture.