Level-Planarity: Transitivity vs. Even Crossings

Abstract

Fulek et al. (2013, 2016, 2017) have presented Hanani-Tutte results for (radial) level-planarity, i.e., a graph is (radial) level-planar if it admits a (radial) level drawing where any two independent edges cross an even number of times. We show that the  2-SAT formulation of level-planarity testing due to Randerath et al. (2001) is equivalent to the strong Hanani-Tutte theorem for level-planarity (2013). By elevating this relationship to radial level-planarity, we obtain a novel polynomial-time algorithm for testing radial level-planarity in the spirit of Randerath et al.