A Direct Proof of the Strong Hanani–Tutte Theorem on the Projective Plane

  • Éric Colin de Verdière
  • Vojtěch KalužaEmail author
  • Pavel Paták
  • Zuzana Patáková
  • Martin Tancer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)


We reprove the strong Hanani–Tutte theorem on the projective plane. In contrast to the previous proof by Pelsmajer, Schaefer and Stasi, our method is constructive and does not rely on the characterization of forbidden minors, which gives hope to extend it to other surfaces. Moreover, our approach can be used to provide an efficient algorithm turning a Hanani–Tutte drawing on the projective plane into an embedding.


Graph drawing Graph embedding Hanani–Tutte theorem Projective plane Topological graph theory 



We would like to thank Alfredo Hubard for fruitful discussions and valuable comments.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Éric Colin de Verdière
    • 1
  • Vojtěch Kaluža
    • 2
    Email author
  • Pavel Paták
    • 3
  • Zuzana Patáková
    • 3
  • Martin Tancer
    • 2
  1. 1.CNRS and Département d’informatique, École normale supérieureParisFrance
  2. 2.Department of Applied MathematicsCharles UniversityPragueCzech Republic
  3. 3.Einstein Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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