| Autor: |
Bryant, Darryn, Maenhaut, Barbara, Smith, Benjamin R. |
| Rok vydání: |
2017 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
In contrast with Kotzig's result that the line graph of a $3$-regular graph $X$ is Hamilton decomposable if and only if $X$ is Hamiltonian, we show that for each integer $k\geq 4$ there exists a simple non-Hamiltonian $k$-regular graph whose line graph has a Hamilton decomposition. We also answer a question of Jackson by showing that for each integer $k\geq 3$ there exists a simple connected $k$-regular graph with no separating transitions whose line graph has no Hamilton decomposition. |
| Databáze: |
arXiv |
| Externí odkaz: |
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