New attack on Kotzig's conjecture
<p>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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
2016-10-01
|
| Series: | Electronic Journal of Graph Theory and Applications |
| Subjects: | |
| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/132 |
| Summary: | <p>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 $n$.</p> |
|---|---|
| ISSN: | 2338-2287 |