2 research outputs found
On Hamilton Decompositions of Line Graphs of Non-Hamiltonian Graphs and Graphs without Separating Transitions
In contrast with Kotzig's result that the line graph of a -regular graph
is Hamilton decomposable if and only if is Hamiltonian, we show that
for each integer there exists a simple non-Hamiltonian -regular
graph whose line graph has a Hamilton decomposition. We also answer a question
of Jackson by showing that for each integer there exists a simple
connected -regular graph with no separating transitions whose line graph has
no Hamilton decomposition