New attack on Kotzig's conjecture

Christian Barrientos (Department of Mathematics Clayton State University, USA)
Sarah M. Minion (Department of Mathematics Clayton State University, USA)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 4, No 2 (2016): Electronic Journal of Graph Theory and Applications

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 $n$.