I'm having problems finding the right words to formulate the following class of graphs in a definition. I'm defining a class of plane graphs with the following properties:
- Removing any vertex of the outer face will not make the graph disconnected
- Removing any two vertices not in the outer face will not make the graph disconnected.
The best definition I could find for now is to say $G$ is 2-connected on the outer face and 3-connected everywhere else.