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Graphs of given genus and arbitrarily large maximum genus

✍ Scribed by Richard D. Ringeisen

Publisher: Elsevier Science
Year: 1973
Tongue: English
Weight: 540 KB
Volume: 6
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(73)90047-2

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✦ Synopsis

Abstrart. The maximum genus of a connected graph (: is the maximum among the genera of a!1 cornpact olientable 2-manifolds upon which G has 2-&l embeddings. In the theorems that fc-llow the use of an edg;:-adding techniq se is combined with ihe well-known Edmonds' technique to prfiruce the desired results. Planar graphs of arbitrarily large maximum genus are disrlayed in Theorem 1. Theorem 2 shows that the possibililty for arbitrarily large difference be-tlMeon genus and maximu>n genus is not limited to planar graphs. In particular, we show that the l):QeeY grqph, the standard maximal planar graph, and the prism graph are upper embeddable. We then show that given ~VZ akld n, there is a graph of genus n and maximum genus larger ihnn mn.

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