  Consider a bicolored point set $P$ in general position in the plane
consisting of $n$ blue and $n$ red points. We show that if a subset of the red
points forms the vertices of a convex polygon separating the blue points, lying
inside the polygon, from the remaining red points, lying outside the polygon,
then the points of $P$ can be connected by non-crossing straight-line segments
so that the resulting graph is a properly colored closed Hamiltonian path.
