Hanani-Tutte for radial planarity Journal Article

Author(s): Fulek, Radoslav; Pelsmajer, Michael; Schaefer, Marcus
Article Title: Hanani-Tutte for radial planarity
Affiliation IST Austria
Abstract: A drawing of a graph G is radial if the vertices of G are placed on concentric circles C 1 , . . . , C k 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 Toth.
Journal Title: Journal of Graph Algorithms and Applications
Volume: 21
Issue 1
ISSN: 1526-1719
Publisher: Department of Computer Science at Brown University  
Date Published: 2017-01-01
Start Page: 135
End Page: 154
DOI: 10.7155/jgaa.00408
Notes: The research of the first author 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 [291734].
Open access: yes (OA journal)
IST Austria Authors
  1. Radoslav Fulek
    14 Fulek
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