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Fáry Theorem

Fáry's theorem states that any simple planar graph can be drawn in a planar straight line embedding, i.e., using straight line segments for edges, none of which cross.

The theorem was independently proved by Steinitz and Rademacher (1934), Wagner (1936), Fáry (1948), and Stein (1951).

See also

Planar Graph, Planar Straight Line Embedding, Steinitz's Theorem

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References

Brandenburg, F. J. "Straight-Line Drawings of 1-Planar Graphs." 3 Sep 2021. https://arxiv.org/abs/2109.01692.Bryant, V. W. "Straight Line Representation of Planar Graphs." Elem. Math. 44, 64-66, 1989.Fáry, I. "On Straight-Line Representation of Planar Graphs." Acta Sci. Math. (Szeged) 11, 229-233, 1948.Scheinerman, E. and Wilf, H. S. "The Rectilinear Crossing Number of a Complete Graph and Sylvester's 'Four Point' Problem of Geometric Probability." Amer. Math. Monthly 101, 939-943, 1994.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 100 and 251, 1990.Stein, S. K. "Convex Maps." Proc. Amer. Math. Soc. 2, 464-466, 1951.Steinitz, E. and Rademacher, H. Vorlesungen über die Theorie der Polyeder. Berlin, Germany: Julius Springer, 1934.Wagner, K. "Bemerkungen zum Vierfarbenproblem." Jahresber. Deutschen Math.Verein. 46, 26-32, 1936.

Cite this as:

Weisstein, Eric W. "Fáry Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FaryTheorem.html

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