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The orientable genus is nonadditive

✍ Scribed by Dan Archdeacon

Publisher: John Wiley and Sons
Year: 1986
Tongue: English
Weight: 760 KB
Volume: 10
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190100314

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✦ Synopsis

A graph G is a k-amalgamation of two graphs G1 and G2 if G = G1 u G2 and GI n G2 is a set of k vertices. In this paper we construct 3-amalgamations G, = H, U H, such that y(G,) = 5n and y(H,) = 3n. where y denotes the orientable genus of a graph. Thus y(Gl U G2) may differ from y ( G l ) + y(G2) by an arbitrarily large amount for amalgamations over 3 (or more) vertices. In contrast, an earlier paper shows that the nonorientable genus of a k-amalgamation differs from the sum of the nonorientable genera of its parts by at most a quadratic on k.

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