  Motivated by a result of [1] which states that if F is a subgraph of a convex
complete graph K_n and F contains no boundary edge of K_n and |E(F)| \leq n-3,
then K_n - F admits a triangulation, we determine necessary and sufficient
conditions on F with |E(F)| \leq n-1 for which the conclusion remains true. For
|E(F)| \geq n, we investigate the possibility of packing F in K_n such that K_n
-F admits a triangulation for certain families of graphs F. These results are
then applied to determine the convex skewness of the convex graphs of the form
K_n - F.
