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

R. Fulek, J. Kynčl, Combinatorica (2019).


Journal Article | Epub ahead of print | English
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Abstract
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.
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2019-10-29
Journal Title
Combinatorica
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Fulek R, Kynčl J. Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica. 2019. doi:10.1007/s00493-019-3905-7
Fulek, R., & Kynčl, J. (2019). Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica. https://doi.org/10.1007/s00493-019-3905-7
Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4.” Combinatorica, 2019. https://doi.org/10.1007/s00493-019-3905-7.
R. Fulek and J. Kynčl, “Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4,” Combinatorica, 2019.
Fulek R, Kynčl J. 2019. Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica.
Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4.” Combinatorica, Springer Nature, 2019, doi:10.1007/s00493-019-3905-7.

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