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An upward embedding of a digraph (directed graph) on the plane or
a surface is an embedding of its underlying graph so that all
directed edges are monotonic and point to a fixed direction. Such
embedding in some literatures is called upward drawing without
crossing of edges. For a given digraph $G$ to decide whether it
has an upward embedding on the plane is known as an NP-Complete
problem (cf. [6,4]). In this paper we study the problem of upward
embedding of digraphs on the round sphere. We shall present a
characterization of all spherical digraphs.
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