Cactus

Cactus --- кактус, дерево Хусими.

A graph $G$ is a сactus if every its edge is a part of at most one cycle in $G$. Cactus graphs are outerplanar since they cannot contain $K_{4}$ or $K_{2,3}$ as a minor. Cactus graphs have treewidth $\leq 2$.