Simple cubic graphs with no short traveling salesman tour

Let $tsp(G)$ denote the length of a shortest travelling salesman tour in a graph $G$. We prove that for any $\epsilon >0$, there exists a simple $2$-connected planar cubic graph $G_1$ such that $tsp(G_1)\ge (1.25-\varepsilon)\cdot|V(G_1)|$,asimple$2$-connectedbipartitecubicgraph$G_2$suchthat$tsp(G_2)\ge (1.2-\varepsilon)\cdot|V(G_2)|$,andasimple$3$-connectedcubicgraph$G_3$suchthat$tsp(G_3)\ge (1.125-\varepsilon)\cdot|V(G_3)|$.