Five Cycle Double Covers of Some Cubic Graphs

The main result of this paper can be roughly described as follows. Any bridgeless cubic graph G having a 2-factor with at most two odd components has a 5-cycle double cover, ie., there exists a collection L of five Eulerian subgraphs of G such that every edge of G is an edge of exactly two subgraphs in L. This generalizes and improves several known results. For instance, we can show that any graph with a Hamilton path has a 5-cycle double cover.