Surfaces, Tree-Width, Clique-Minors, and Partitions

@article{Ding2000SurfacesTC,
  title={Surfaces, Tree-Width, Clique-Minors, and Partitions},
  author={Guoli Ding and Bogdan Oporowski and Daniel P. Sanders and Dirk L. Vertigan},
  journal={J. Comb. Theory, Ser. B},
  year={2000},
  volume={79},
  pages={221-246}
}
In 1971, Chartrand, Geller, and Hedetniemi conjectured that the edge set of a planar graph may be partitioned into two subsets, each of which induces an outerplanar graph. Some partial results towards this conjecture are presented. One such result, in which a planar graph may be thus edge partitioned into two series-parallel graphs, has nice generalizations for graphs embedded onto an arbitrary surface and graphs with no large clique-minor. Several open questions are raised. 
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