Abstract
Kao recently proved that all general directed graphs have directed cycle separators of any size. In contrast, Miller proved that planar undirected graphs with n vertices and maximum face size d have O( dn ) -size undirected cycle separators. Therefore it is important to investigate whether a planar directed graph has a small-size directed cycle separator. This paper shows that certain important classes of planar directed graphs have no sublinear-size directed cycle separators.
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