Hamilton Cycle Decomposition of Line Graphs and a Conjecture of Bermond

In this paper it is proved that if a graph G has a decomposition into an even (resp., odd) number of Hamilton cycles, then L(G), the line graph of G, has a decomposition into Hamilton cycles (reap., Hamilton cycles and a 2-Factor). Further, we show that if G is a 2k-regular graph having a Hamilton cycle, then L(G) has a decomposition into Hamilton cycles and a 2-factor. These results generalize a result of Jaeger and also support the following conjecture of Bermond: If G has a Hamilton cycle decomposition, then L(G) can be decomposed into Hamilton cycles.