Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs
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.
|Keywords||chordal graph, elimination ordering, maximal outerplanar graph, path-neighborhood graph, triangle graph|
|Publisher||Erasmus School of Economics (ESE)|
Laskar, R.C., Mulder, H.M., & Novick, B., B.. (2011). Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs (No. EI 2011-16). Report / Econometric Institute, Erasmus University Rotterdam (pp. 1–12). Erasmus School of Economics (ESE). Retrieved from http://hdl.handle.net/1765/23560