Strong Hanani-Tutte for the Torus

Fulek, Radoslav; Pelsmajer, Michael J.; Schaefer, Marcus

doi:10.48550/arxiv.2009.01683

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2022

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“…Both the weak and the strong Hanani-Tutte theorem have been established for radial level-planarity [11,10]. Further, the weak version has been shown for all surfaces [23] and the strong version on the Torus [12] and the projective plane [22]. A counterexample for the strong version is known on the orientable surface of genus 4 [9].…”

Section: Introductionmentioning

confidence: 94%

Level-Planarity: Transitivity vs. Even Crossings

Brückner

Rutter

Stumpf

2022

Electron. J. Combin.

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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.

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