BIRS Workshop Lecture Videos
Counterexample to the Hanani-Tutte theorem on the surface of genus 4 Kyncl, Jan
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 generalized to the orientable surface of genus 4. As a base step in the construction we use a counterexample to the unified Hanani-Tutte theorem on the torus. The result was obtained together with Radoslav Fulek.
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