Abstract
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.
This research began at the Blue Mountains Workshop on Geometric Graph Theory, August, 2010, in Australia, and supported by the University of Sydney IPDF funding and the ARC (Australian Research Council). Hong is supported by ARC Future Fellowship. Liotta is also supported by the Italian Ministry of Education, University, and Research (MIUR) under PRIN 2012C4E3KT AMANDA. For the full version of this paper with proofs, see [6].
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Eades, P., Hong, SH., Liotta, G., Katoh, N., Poon, SH. (2015). Straight-Line Drawability of a Planar Graph Plus an Edge. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_25
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DOI: https://doi.org/10.1007/978-3-319-21840-3_25
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