Let $G=(V,E)$, an un-directed graph. Find an efficient algorithm to return a $U\subseteq V$, where $u\in U$ is in some simple cycle of $G$.
So basically we've learned in class about the $low$ indicator, which defined as follows: $$low[v] = \min\begin{cases} d[v]\\ d[u], (v,u) \text{ is a back-edge}\\ d[u], u \text{ is child of v in the DFS tree} \end{cases}$$
Note: Here, $d[v]$ is the time of discovering the edge $v$ during the DFS scan.
I need to somehow utilize this indicator. More precisely, running DFS scan and updating this indicator for every vertex. Then, I need to come up with some rule to identify vertices which are part of some simple cycle.
Here below I've attached an example for every vxertex $v[x][y]$, $x$ identifies the discovery time and $y$ identifies the $low$ value of $v$.
I can't see a rule\ pattern and will be glad for an idea.
Thanks.