Geodesic
Unified Hanani-Tutte theorem
The electronic journal of combinatorics, Tome 24 (2017) no. 3
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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.
DOI : 10.37236/6663
Classification : 05C10, 05C62, 68R10
Mots-clés : Hanani-Tutte theorem, planar graph, rotation system 
@article{10_37236_6663,
     author = {Radoslav Fulek and Jan Kyn\v{c}l and D\"om\"ot\"or P\'alv\"olgyi},
     title = {Unified {Hanani-Tutte} theorem},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {3},
     doi = {10.37236/6663},
     zbl = {1369.05045},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6663/}
}
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Radoslav Fulek; Jan Kynčl; Dömötör Pálvölgyi. Unified Hanani-Tutte theorem. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6663

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