Transversals of Longest Paths

Let $\text{lpt}(G)$ be the minimum cardinality of a set of vertices that intersects all longest paths in a graph $G$. Let $\omega (G)$ be the size of a maximum clique in $G$, and $\text{tw}(G)$ be the treewidth of $G$. We prove that $ \lpt(G) \leq \max{1,\omega(G)-2}$when$G$isaconnectedchordalgraph;that$\lpt(G) =1$when$G$ is a connected bipartite permutation graph or a connected full substar graph; and that $\text{lpt}(G)\le \text{tw}(G)$ for any connected graph $G$.