Soppose we have an udirected, connected graph. Apply the DFS algorithm to find back edges of this graph. Now, I have found a lecture notes saying following :
Each back edge (i,j) defines a cycle. A cycle consists of the back edge (i,j) and unique tree edges forming the path from j to i. The cycles so defined by the back edges form a cycle base of the graph. Every cycle of the graph is the union (exclusive OR) of two or more cycles from this cycle base.
Can I conclude from this that every simple cycle in this graph will contain at least one back edge?