On the number of labeled outerplanar $k$-cyclic bridgeless graphs

We obtain an explicit formula for the number of labeled connected outerplanar $k$-cyclic $n$-vertex bridgeless graphs. We find asymptotics for the number of those graphs for a large number of vertices and fixed $k$. As a consequence, we prove that, for $k$ fixed, almost all labeled connected outerplanar $k$-cyclic graphs have bridges. Tab. 1, bibliogr. 14.