Outerplanar graph

Outerplanar graph --- внешнепланарный граф.

A graph $G$ is outerplanar if there is a crossing-free embedding of $G$ in the plane such that all vertices are on the same face. $G$ is outerplanar iff $G$ contains no subgraph homeomorphic to $K_{4}$ or $K_{2,3}$ by a homeomorphism that deletes degree-2 vertices but does not add them.

$G$ is $k$-outerplanar if for $k = 1$ $G$ is an outerplanar graph and for $k > 1$ $G$ has a planar embedding such that if all vertices on the exterior face are deleted, the connected components of the remaining graph are all $(k-1)$-outerplanar. See also Halin graph.