Fáry's Theorem for 1-Planar Graphs

  title={F{\'a}ry's Theorem for 1-Planar Graphs},
  author={Seok-Hee Hong and Peter Eades and Giuseppe Liotta and Sheung-Hung Poon},
Fáry’s theorem states that every plane graph can be drawn as a straightline drawing. A plane graph is a graph embedded in a plane without edge crossings. In this paper, we extend Fáry’s theorem to non-planar graphs. More specifically, we study the problem of drawing 1-plane graphs with straight-line edges. A 1-plane graph is a graph embedded in a plane with at most one crossing per edge. We give a characterisation of those 1-plane graphs that admit a straight-line drawing. The proof of the… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 14 references

Linear time algorithms for convex drawings of planar graphs, Progress in Graph Theory, Academic Press, pp

  • N. Chiba, T. Yamanouchi, T. Nishizeki
  • 153-173,
  • 1984
Highly Influential
7 Excerpts

and M

  • T. Nishizek
  • S. Rahman, Planar Graph Drawing, World Scientific…
  • 2004
2 Excerpts

and I

  • G. Di Battista, P. Eades, R. Tamassi
  • G. Tollis, Graph Drawing: Algorithms for the…
  • 1999
2 Excerpts

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