Abstract
The (outer) planar coarseness of a graph is the largest number of pairwise-edge-disjoint non-(outer)planar subgraphs. It is shown that the maximum outerplanar coarseness, over all $n$-vertex planar graphs, lies in the interval $\;\big [\lfloor (n-2)/3 \rfloor, \lfloor (n-2)/2 \rfloor \big ]$.
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