1. ## graph theory question about walks and cycles

If a graph $G$ has a closed walk of length at least three containing a vertex $x$, then $G$ has a cycle
containing $x$.

Can anyone explain why this statement is true or false?

2. Originally Posted by lachicacomica
If a graph $G$ has a closed walk of length at least three containing a vertex $x$, then $G$ has a cycle
containing $x$.

Can anyone explain why this statement is true or false?
Look at the definition of a closed walk and cycle. How do they compare?