The first problem states that if $G$ is a graph with $n$ vertices and at least $2n-2$ edges then $G$ must contain two distinct cycles of the same length.
The second problem shows that if $G$ has at least $n+4$ edges then it must contain two disjoint cycles.
My question now is
Question. What would be a lower bound for the number of edges in a graph that would force the graph to contain two disjoint cycles of same length?
By distinct cycles $C_1,C_2$ we mean that $E(C_1) \cap E(C_2) \ne E(C_1) \cup E(C_2)$ and we say that they are disjoint if $E(C_1) \cap E(C_2) = \emptyset$