On Hamilton Decompositions of Line Graphs of Non-Hamiltonian Graphs and Graphs without Separating Transitions
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2017
- DOI:
- 10.48550/arXiv.1710.06037
- arXiv:
- arXiv:1710.06037
- Bibcode:
- 2017arXiv171006037B
- Keywords:
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- Mathematics - Combinatorics;
- 05C45;
- 05C51;
- 05C70