The Minor Crossing Number of Graphs with an Excluded Minor - Bokal, Drago; Fijavž, Gašper; Wood, David R. (The Electronic Journal of Combinatorics, 2008)
The minor crossing number of a graph $G$ is the minimum crossing number of a graph that contains $G$ as a minor. It is proved that for every graph $H$ there is a constant $c$, such that every graph $G$ with no $H$-minor has minor crossing number at most $c|V(G)|$.