Fulek, RadoslavIST Austria ; Pelsmajer, Michael ; Schaefer, Marcus
A drawing of a graph G is radial if the vertices of G are placed on concentric circles C1, . . . , Ck with common center c, and edges are drawn radially: every edge intersects every circle centered at c at most once. G is radial planar if it has a radial embedding, that is, a crossing- free radial drawing. If the vertices of G are ordered or partitioned into ordered levels (as they are for leveled graphs), we require that the assignment of vertices to circles corresponds to the given ordering or leveling. We show that a graph G is radial planar if G has a radial drawing in which every two edges cross an even number of times; the radial embedding has the same leveling as the radial drawing. In other words, we establish the weak variant of the Hanani-Tutte theorem for radial planarity. This generalizes a result by Pach and Tóth.
The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no .
99 - 110
GD: Graph Drawing and Network Visualization
Los Angeles, CA, USA
2015-09-24 – 2015-09-26
Fulek R, Pelsmajer M, Schaefer M. Hanani-Tutte for radial planarity. In: Vol 9411. Springer; 2015:99-110. doi:10.1007/978-3-319-27261-0_9
Fulek, R., Pelsmajer, M., & Schaefer, M. (2015). Hanani-Tutte for radial planarity (Vol. 9411, pp. 99–110). Presented at the GD: Graph Drawing and Network Visualization, Los Angeles, CA, USA: Springer. https://doi.org/10.1007/978-3-319-27261-0_9
Fulek, Radoslav, Michael Pelsmajer, and Marcus Schaefer. “Hanani-Tutte for Radial Planarity,” 9411:99–110. Springer, 2015. https://doi.org/10.1007/978-3-319-27261-0_9.
R. Fulek, M. Pelsmajer, and M. Schaefer, “Hanani-Tutte for radial planarity,” presented at the GD: Graph Drawing and Network Visualization, Los Angeles, CA, USA, 2015, vol. 9411, pp. 99–110.
Fulek R, Pelsmajer M, Schaefer M. 2015. Hanani-Tutte for radial planarity. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411. 99–110.
Fulek, Radoslav, et al. Hanani-Tutte for Radial Planarity. Vol. 9411, Springer, 2015, pp. 99–110, doi:10.1007/978-3-319-27261-0_9.