On the Turán Number of Generalized Theta Graphs

Let $Θ_{k_1,\cdots,k_\ell}$ denote the generalized theta graph, which consists of $\ell$ internally disjoint paths with lengths $k_1,\cdots, k_{\ell}$, connecting two fixed vertices. We estimate the corresponding extremal number $\text{ex}(n,Θ_{k_1,\cdots,k_\ell})$. When the lengths of all paths hav