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Minor-monotone crossing number

Abstract : The minor crossing number of a graph $G$, $rmmcr(G)$, is defined as the minimum crossing number of all graphs that contain $G$ as a minor. We present some basic properties of this new minor-monotone graph invariant. We give estimates on mmcr for some important graph families using the topological structure of graphs satisfying \$mcr(G) ≤k$.
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https://hal.inria.fr/hal-01184390
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Drago Bokal, Gašper Fijavž, Bojan Mohar. Minor-monotone crossing number. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.123-128. ⟨hal-01184390⟩

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