Geodesic
Rotation systems and simple drawings in surfaces
Rosna Paul1 ; Gelasio Salazar2 ; Alexandra Weinberger3
1Institute of Software Technology, Graz University of Technology, Austria
2Instituto de Física, Universidad Autónoma de San Luis Potosí, SLP 78000, Mexico
3Fernuniversität in Hagen
The electronic journal of combinatorics, Tome 31 (2024) no. 2
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Every simple drawing of a graph in the plane naturally induces a rotation system, but it is easy to exhibit a rotation system that does not arise from a simple drawing in the plane. We extend this to all surfaces: for every fixed surface $\Sigma$, there is a rotation system that does not arise from a simple drawing in $\Sigma$.
DOI : 10.37236/11368
Classification : 05C62
Mots-clés : drawing of a graph in an orientable surface, rotation

Rosna Paul  1   ; Gelasio Salazar  2   ; Alexandra Weinberger  3

1 Institute of Software Technology, Graz University of Technology, Austria
2 Instituto de Física, Universidad Autónoma de San Luis Potosí, SLP 78000, Mexico
3 Fernuniversität in Hagen 
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     author = {Rosna Paul and Gelasio  Salazar and Alexandra  Weinberger},
     title = {Rotation systems and simple drawings in surfaces},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {2},
     doi = {10.37236/11368},
     zbl = {1543.05141},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11368/}
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Rosna Paul; Gelasio  Salazar; Alexandra  Weinberger. Rotation systems and simple drawings in surfaces. The electronic journal of combinatorics, Tome 31 (2024) no. 2. doi: 10.37236/11368

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