  For a graph $H$ consisting of finitely many internally disjoint paths
connecting two vertices, with possibly distinct lengths, we estimate the
corresponding extremal number $\text{ex}(n,H)$. When the lengths of all paths
have the same parity, $\text{ex}(n,H)$ is $O(n^{1+1/k^\ast})$, where $2k^\ast$
is the size of the smallest cycle which is included in $H$ as a subgraph.
