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The crossing number of a graph is the minimum number of crossings in adrawing of the graph in the plane. Our main result is that every graph $G$ thatdoes not contain a fixed graph as a minor has crossing number $O(\Delta n)$,where $G$ has $n$ vertices and maximum degree $\Delta$. This dependence on $n$and $\Delta$ is best possible. This result answers an open question of Wood andTelle [New York J. Mathematics, 2007], who proved the best previous bound of$O(\Delta^2 n)$. We also study the convex and rectilinear crossing numbers, andprove an $O(\Delta n)$ bound for the convex crossing number of boundedpathwidth graphs, and a $\sum_v\deg(v)^2$ bound for the rectilinear crossingnumber of $K_{3,3}$-minor-free graphs.

Tight Upper Bounds on the Crossing Number in a Minor-Closed Class