  We tackle the problem of constructing increasing-chord graphs spanning point
sets. We prove that, for every point set P with n points, there exists an
increasing-chord planar graph with O(n) Steiner points spanning P. Further, we
prove that, for every convex point set P with n points, there exists an
increasing-chord graph with O(n log n) edges (and with no Steiner points)
spanning P.
