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

09/01/2017

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by   Radoslav Fulek, et al.

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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.