Formulation
The usual formulation of the cycle double cover conjecture asks whether every bridgeless undirected graph has a collection of cycles such that each edge of the graph is contained in exactly two of the cycles. The requirement that the graph be bridgeless is an obvious necessary condition for such a set of cycles to exist, because a bridge cannot belong to any cycle. A collection of cycles satisfying the condition of the cycle double cover conjecture is called a cycle double cover. Some graphs such as cycle graphs and bridgeless cactus graphs can only be covered by using the same cycle more than once, so this sort of duplication is allowed in a cycle double cover.
Read more about this topic: Cycle Double Cover
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