Outerplanar Coarseness of Planar Graphs

Paul C. Kainen

doi:10.35834/mjms/1474295359

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Home > Journals > Missouri J. Math. Sci. > Volume 28 > Issue 1 > Article

May 2016 Outerplanar Coarseness of Planar Graphs

Paul C. Kainen

Missouri J. Math. Sci. 28(1): 97-98 (May 2016). DOI: 10.35834/mjms/1474295359

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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 $\;\big [\lfloor (n-2)/3 \rfloor, \lfloor (n-2)/2 \rfloor \big ]$.