A planar straight line embedding of a planar graph is a planar embedding in which only straight
line segments are used to connect the graph vertices.
The Fáry theorem established that every planar graph has a planar straight line embedding with
noncrossing edges (Bryant 1989; Skiena 1990, pp. 100 and 251; Scheinerman and
Wilf 1994), and such embeddings (with rectilinear
crossing number 0) are sometimes known as a Fáry embedding.
de Fraysseix et al. (1988) give an algorithm for constructing a planar straight line embedding for a planar graph of order by placing the vertices on a grid (Skiena 1990, p. 251).
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