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. A pair of edges e and f in a graph is independent if e and f do not share a vertex. We show that a graph G is radial planar if G has a radial drawing in which every two independent edges cross an even number of times; the radial embedding has the same leveling as the radial drawing. In other words, we establish the strong Hanani-Tutte theorem for radial planarity. This characterization yields a very simple algorithm for radial planarity testing.
CITATION STYLE
Fulek, R., Pelsmajer, M., & Schaefer, M. (2016). Hanani-Tutte for radial planarity II. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9801 LNCS, pp. 468–481). Springer Verlag. https://doi.org/10.1007/978-3-319-50106-2_36
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