Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4
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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.
Mathematics Subject Classification (2010)05C10 57M15
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