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The maximum rectilinear crossing number of a graph $G$ is the maximum numberof crossings in a good straight-line drawing of $G$ in the plane. In a gooddrawing any two edges intersect in at most one point (counting endpoints), nothree edges have an interior point in common, and edges do not contain verticesin their interior. A spider is a subdivision of $K_{1,k}$. We provide bothupper and lower bounds for the maximum rectilinear crossing number of spiders.While there are not many results on the maximum rectilinear crossing numbers ofinfinite families of graphs, our methods can be used to find the exact maximumrectilinear crossing number of $K_{1,k}$ where each edge is subdivided exactlyonce. This is a first step towards calculating the maximum rectilinear crossingnumber of arbitrary trees.

A Note on the Maximum Rectilinear Crossing Number of Spiders