Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4

Abstrakt

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.

Klíčová slova

• Hanani-Tutte theorem
• unified Hanani-Tutte theorem
• orientable surface