Straight-Line Drawability of a Planar Graph Plus an Edge
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.
KeywordsHamilton Path External Face Clockwise Order Edge Crossing Closed Walk
Unable to display preview. Download preview PDF.
- 1.Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall (1999)Google Scholar
- 4.Chiba, N., Yamanouchi, T., Nishizeki, T.: Linear algorithms for convex drawings of planar graphs. In: Progress in Graph Theory, pp. 153–173. Academic Press, London (1984)Google Scholar
- 6.Eades, P., Hong, S.H., Liotta, G., Katoh, N., Poon, S.H.: Straight-line drawability of a planar graph plus an edge (2015). ArXiv, 1504.06540Google Scholar
- 12.Nagamochi, H.: Straight-line drawability of embedded graphs. Technical Report 2013–005, Graduate School of Informatics, Kyoto University (2013)Google Scholar