Graphs with forbidden subgraphs . Journal of Combinatorial Theory Ser. This last section is devoted to some results which cannot be subsumed under a general topic. Chatrand, G., D. Geller, and S. Hedetniemi, Graphs with forbidden subgraphs , J. Comb. Another example is the minimum cost flow problem.
Every planar graph has an edge partition into two outerplanar graphs.
Thus there are graphs of arbitrarily large tree width that are embeddable on every surface. Also, Theorem 2.2 shows that every planar graph can be edge partitioned into two partial 2 trees. G. Chartrand, D. Geller, and S. Hedetniemi, Graphs with forbidden subgraphs , J. Combin. G. Chartrand, D. Geller and S. Hedetniemi, Graphs with forbidden subgraphs , J. Combin. Odense University Odense, Denmark btoft imada.ou.