Every planar graph has an edge partition into two outerplanar graphs.
1 See the acknowledgments section at the end of the paper to see the grant support of the authors. This section obtains results showing that graphs on surfaces have vertex and edge partitions into graphs of low tree width. For non planar graphs on surfaces of low genus, finding a large planar subgraph is useful. C.J. Colbourn and E.S. Elmallah, Partitioning the edges of a planar graph into two partial k-trees , Congr.