Generating Cycles

A vertex-induced subgraph of a simple graph $G$ is one that can be obtained from $G$ by removing some (possibly, none) vertices. When a vertex is removed, all edges incident to it must also be removed. A vertex-induced cycle is a vertex-induced subgraph that is also a cycle. Equivalently, a cycle $C$ is vertex induced, if for every edge $e$ in the graph $G$ that does not belong to $C$, **at most