Abstract :
In this paper, we obtained some necessary and sufficient conditions for a graph having 5-, 6- and 7-cycle double covers, etc. We also provide a few necessary and sufficient conditions for a graph admitting a nowhere-zero 4-flow. With the aid of those basic properties of nowhere-zero 4-flow and the result about 5-cycle double cover, we are able to prove that each 2-edge-connected graph with one edge short of admitting a nowhere-zero 4-flow has a 5-cycle double cover which is a generalization of a theorem due to Huck and Kochol (JCTB, 1995) for cubic graphs.
