Surfaces, Tree-Width, Clique-Minors, and Partitions
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. © 2000 Academic Press.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
Ding, G., Oporowski, B., Sanders, D., & Vertigan, D. (2000). Surfaces, Tree-Width, Clique-Minors, and Partitions. Journal of Combinatorial Theory. Series B, 79 (2), 221-246. https://doi.org/10.1006/jctb.2000.1962