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Unique and faithful embeddings of projective-planar graphs

✍ Scribed by Seiya Negami

Publisher: John Wiley and Sons
Year: 1985
Tongue: English
Weight: 393 KB
Volume: 9
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190090206

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✦ Synopsis

A graph G is uniquelyembeddable in a surface f 2 if for any two embeddings f,,f2 : G + f 2 , there exists an isomorphism u : G + G and a homeo-

admits an embedding f : G + F2 such that for any isomorphism (T : G + G, there is a homeomorphism h : F 2 f 2 with h . f = f . u. It will be shown that if a projective-planar graph G is 5-connected and contains a subdivision of the complete graph K6 as its subgraph, then G is uniquely embeddable in a projective plane, and that moreover if G is not isomorphic to K6, then G is faithfully embeddable in a projective plane.

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