  Motivated by a result of [17], we determine necessary and sufficient
conditions on $F\/$ with $|E(F)| \leq n-1\/$ for which $K_n - F\/$ admits a
$g$-angulation. For $|E(F)| \geq n\/$, we investigate the possibility of
placing $F\/$ in $K_n\/$ such that $K_n -F\/$ admits a $g$-angulation for
certain families of graphs $F\/$.
