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Projective plane embeddings of polyhedral pinched maps

✍ Scribed by Adrian Riskin

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 607 KB
Volume: 126
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90272-0

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✦ Synopsis

We give various conditions on pinched-torus polyhedral maps which are necessary for their graphs to be embeddable in the projective plane. Our other main result is that even if the graph of a polyhedral map in the pinched torus is embeddable in a projective plane, the map induced by the embedding cannot be polyhedral, but must have all faces bounded by cycles. Finally, we give a class of examples of graphs which have polyhedral embeddings on the pinched torus and also on orientable surfaces of arbitrary high genus.

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