New attack on Kotzig's conjecture

In this paper we study a technique to transform α-labeled trees into ρ-labeled forests. We use this result to prove that the complete graph K2n+1 can be decomposed into these types of forests. In addition we show a robust family of trees that admit ρ-labelings, we use this result to describe the set of all trees for which a ρ-labeling must be found to completely solve Kotzig’s conjecture about decomposing cyclically the complete graph K2n+1 into copies of any tree of size n.