 Note that since every planar graph has at most O(n) faces, any further improvement of this result, will imply an improvement upon Rao's long standing upper bound.
<coherence>  Note that since every planar graph has at most O(n) faces, any further improvement of this result, will imply an improvement upon Rao's long standing upper bound.
 Since every planar graph has at most O(n) faces, any further improvement of this result, will imply an improvement upon Rao's long standing upper bound.