Hanani-Tutte for Radial Planarity II

  • Radoslav Fulek
  • Michael Pelsmajer
  • Marcus Schaefer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

Abstract

A drawing of a graph G is radial if the vertices of G are placed on concentric circles \(C_1, \ldots , C_k\) 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. 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.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Radoslav Fulek
    • 1
  • Michael Pelsmajer
    • 2
  • Marcus Schaefer
    • 3
  1. 1.IST AustriaKlosterneuburgAustria
  2. 2.Illinois Institute of TechnologyChicagoUSA
  3. 3.DePaul UniversityChicagoUSA

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