Unified Hanani Tutte theorem - Fulek, Radoslav; Kynčl, Jan; Pálvölgyi, Dömötör; International IST Postdoc Fellowship Programme (Electronic Journal of Combinatorics, 2017)
We introduce a common generalization of the strong Hanani–Tutte theorem and the weak Hanani–Tutte theorem: if a graph G has a drawing D in the plane where every pair of independent edges crosses an even number of times, then G has a planar drawing preserving the rotation of each vertex whose incident edges cross each other evenly in D. The theorem is implicit in the proof of the strong Hanani–Tutte theorem by Pelsmajer, Schaefer and Štefankovič. We give a new, somewhat simpler proof.
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Keywords: article