Page 16 - Ellingham, Mark, Mariusz Meszka, Primož Moravec, Enes Pasalic, 2014. 2014 PhD Summer School in Discrete Mathematics. Koper: University of Primorska Press. Famnit Lectures, 3.
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.1 Embeddings of graphs
Surfaces can also be represented in other ways as polygons with identified sides, e.g.
‘usual’ representation of Klein bottle is not standard one.
Planar representation with handle or crosscap gadgets: Can also represent surfaces in
plane: think of sphere as plane with implicit point at infinity, then add handles or
crosscaps which we treat as ‘gadgets’ allowing curves to cross in certain ways.
We can mix the above two representations: use polygon representation and then add
handles or crosscaps.
Surfaces can also be represented in other ways as polygons with identified sides, e.g.
‘usual’ representation of Klein bottle is not standard one.
Planar representation with handle or crosscap gadgets: Can also represent surfaces in
plane: think of sphere as plane with implicit point at infinity, then add handles or
crosscaps which we treat as ‘gadgets’ allowing curves to cross in certain ways.
We can mix the above two representations: use polygon representation and then add
handles or crosscaps.
