Maximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph T(G) has the triangles of the graph G as its vertices, two of these being adjacent whenever as triangles in G they share an edge. A graph is edge-triangular if every edge is in at least one triangle. The main results can be summarized as follows: the class of maximal outerplanar graphs is precisely the intersection of any of the two following classes: the chordal graphs, the path-neighborhood graphs, the edge-triangular graphs having a tree as triangle graph.
Australasian Journal of Combinatorics
Department of Econometrics

Laskar, R. C., Mulder, M., & Novick, B. (2012). Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs. Australasian Journal of Combinatorics, 52, 185–195. Retrieved from