We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line drawing, and a linear-time drawing algorithm that constructs such a drawing, if it exists. We also show that some almost-planar graphs require exponential area for a straight-line drawing.
CITATION STYLE
Eades, P., Hong, S. H., Liotta, G., Katoh, N., & Poon, S. H. (2015). Straight-line drawability of a planar graph plus an edge. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9214, pp. 301–313). Springer Verlag. https://doi.org/10.1007/978-3-319-21840-3_25
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