Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4

  • Radoslav FulekEmail author
  • Jan Kynčl


We find a graph of genus 5 and its drawing on the orientable surface of genus 4 with every pair of independent edges crossing an even number of times. This shows that the strong Hanani–Tutte theorem cannot be extended to the orientable surface of genus 4. As a base step in the construction we use a counterexample to an extension of the unified Hanani–Tutte theorem on the torus.

Mathematics Subject Classification (2010)

05C10 57M15 


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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2019

Authors and Affiliations

  1. 1.IST AustriaKlosterneuburgAustria
  2. 2.Charles UniversityPragueCzech Republic

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