Drawing disconnected graphs on the Klein bottle

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We prove that two disjoint graphs must always be drawn separately on the Klein bottle, in order to minimize the crossing number of the whole drawing.
13 pages, second version, major changes in the proof

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Combinatorics, 05C10

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http://salesiana.dossiersoluciones.com/handle/123456789/173085

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0810.0508
 http://arxiv.org/abs/0810.0508

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arXiv