# New Attack on Kotzig's Conjecture

Barrientos, Christian • Minion, Sarah M

## 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 $n$.

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