Hello, I'm new to combinatorics so I'm having a bit of trouble. The question I'm having trouble with goes like this:
Let $W=v_0e_1v_1\ldots e_nv_n$ be a walk in a graph $G$, such that $v_0 =v_n$ and all the edges $e_1,\dotsc,e_n$ are distinct. Prove that there exists a set ${C_1,\dotsc,C_m}$ of cycles in $G$ such that ${e_1,\dotsc,e_n}=E(C_1)\cup\ldots\cup E(C_m)$, and $E(C_s)\cap E(C_r) =\emptyset$ for all $s\ne r$.
Any help would be great!