  It is proved that if a graph is regular of even degree and contains a
Hamilton cycle, or regular of odd degree and contains a Hamiltonian $3$-factor,
then its line graph is Hamilton decomposable. This result partially extends
Kotzig's result that a $3$-regular graph is Hamiltonian if and only if its line
graph is Hamilton decomposable, and proves the conjecture of Bermond that the
line graph of a Hamilton decomposable graph is Hamilton decomposable.
