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05896634 Kainen, Paul C. Outerplanar crossing numbers of planar graphs. Bull. Inst. Comb. Appl. 61, 69-76 (2011). 2011 The Institute of Combinatorics and its Applications, Winnipeg EN book crossing numbers convex crossing numbers path powers Summary: The rate of increase of the outerplanar crossing number with number of vertices is studied for planar graphs. It is shown that second and third powers of paths behave, with respect to the outerplanar crossing number, as third and fourth powers do for planar crossings. For $r \ge 3$, the outerplanar crossing number of $\overline K_2 * C_r$ (the graph determined by a sphere with $r$ meridians, the equator, and north and south poles) is shown to be $2r - 4 + \lfloor r/2 \rfloor \lfloor (r-1)/2 \rfloor$, where ``$*$'' denotes graph-join.