New attack on Kotzig's conjecture

Abstract

In this paper we study a technique to transform $\alpha $-labeled trees into  $\rho $-labeled forests. We use this result to prove that the complete graph $K_{2n+1}$ can be decomposed into these types of forests. In addition we show a robust family of trees that admit $\rho $-labelings, we use this result to describe the set of all trees for which a $\rho $-labeling must be found to completely solve Kotzig's conjecture about decomposing cyclically the complete graph $K_{2n+1}$ into copies of any tree of size $n$.