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Recently, Fulek et al. [5,6,7] 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. [14] is equivalent to the strong Hanani-Tutte theorem for level planarity [7]. Further, we show that this relationship carries over to radial level planarity, which yields a novel polynomial-time algorithm for testing radial level planarity.

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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.