Planar Graphs A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the unbounded outside face.
Every planar graph can be edge-partitioned into two outerplanar graphs.
His result implies that every planar graph is the union of three forests. Hence such a graph is the union of three outerplanar graphs. His results also show that every outerplanar graph is the union of two forests, but it is unclear if this helps solve the above conjecture. Note that it suffices to prove the conjecture for triangulations. However, he refutes the stronger conjectures that every planar graph edge-partitions into a forest and an outerplanar graph, or into two outerplanar graphs with the same outer boundary cycle.