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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Christian Barrientos
Department of Mathematics Clayton State University, USA
Electrical & Electronics Engineering

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New attack on Kotzig's conjecture Christian Barrientos; Sarah M. Minion
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 2 (2016): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2016.4.2.1

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 $n$.
Co-Authors Sarah M. Minion