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The nonorientable genus is additive

✍ Scribed by Dan Archdeacon

Publisher
John Wiley and Sons
Year
1986
Tongue
English
Weight
816 KB
Volume
10
Category
Article
ISSN
0364-9024

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✦ Synopsis

A graph G is a k-amalgamation of two graphs G1 and G2 if G = G, U G2 and G1 fl G2 is a set of k vertices. In this paper we show that +(GI differs from +(G1) + j4G2) by at most a quadratic on k, where denotes the nonorientable genus of a graph. In the sequel to this paper we show that no such bound holds for the orientable genus of k-amalgamations.

πŸ“œ SIMILAR VOLUMES

Blocks and the nonorientable genus of gr
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## Abstract Examples are given to show that the nonorientable genus of a graph is not additive over its blocks. A nonorientable analog for the Battle, Harary, Kodama, and Youngs Theorem is proved; this completely determines the nonorientable genus of a graph in terms of its blocks. It is also shown

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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

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Additivity is a useful property of the multiset (or divisors-of-an-integer) poset. It is shown here that another class of poset, which includes the cubical poset, also has this property,