As already noted, planarity is a very mild relaxation of the better known projectivity constraint, the only difference being that planarity allows graphs with covered roots (see Definition 2), and studies of natural language treebanks have shown the vast majority of non-projective structures to be non-planar as well (Kuhlmann and Nivre 2006;Havelka 2007).
8 being able to parse planar dependency graphs only provides a modest improvement in practical coverage with respect to projective parsing.