Cycle Double Cover Conjecture
  In this paper, a proof of the cycle double cover conjecture is presented. The cycle double cover conjecture purports that if a graph is bridgeless, then there exists a list of cycles in the graph such that every edge in the graph appears in the list exactly twice. By applying induction on the number of edges in a bridgeless graph, I show that when an edge is added to a bridgeless graph, we can reform the cycle double cover to include that edge. By mathematical induction, this concludes the general CDC. 
P. Clarke
math.CO