Missouri Journal of Mathematical Sciences

Outerplanar Coarseness of Planar Graphs

Paul C. Kainen

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

Article information

Missouri J. Math. Sci., Volume 28, Issue 1 (2016), 97-98.

First available in Project Euclid: 19 September 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]

coarseness crossing number outerplanar invariants planar graphs


Kainen, Paul C. Outerplanar Coarseness of Planar Graphs. Missouri J. Math. Sci. 28 (2016), no. 1, 97--98. doi:10.35834/mjms/1474295359. https://projecteuclid.org/euclid.mjms/1474295359

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