The class of outerplanar graphs is minor-closed and can be characterized by two excluded minors: (Formula presented.) and (Formula presented.). The class of graphs that contain a vertex whose removal leaves an outerplanar graph is also minor-closed. We provide the complete list of 57 excluded minors for this class.
Publication Source (Journal or Book title)
Graphs and Combinatorics
Ding, G., & Dziobiak, S. (2016). Excluded-Minor Characterization of Apex-Outerplanar Graphs. Graphs and Combinatorics, 32 (2), 583-627. https://doi.org/10.1007/s00373-015-1611-9