Yes, every inner face must be a triangle, as chords drawn outside a cycle prevent a drawing from being outerplanar. Drawings of chordal graphs are then just triangulations of polygons; conversely, every triangulated polygon is outerplanar (certainly) and chordal (by induction, as cycles are sub-[triangulated polygons]).
Ben Barber
- 4.6k
- 2
- 25
- 38