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Nonadditivity of the 1-genus of a graph

โœ Scribed by Vladimir P. Korzhik

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
230 KB
Volume
184
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

The 1-genus of a graph is the smallest possible genus of an orientable surface such that the graph can be drawn on the surface so that each edge is crossed over by no more than one other edge. An example with smallest number of vertices is given showing that the 1-genus of a graph is not additive, i.e.

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## Abstract The cochromatic number of a graph __G__, denoted by __z__(__G__), is the minimum number of subsets into which the vertex set of __G__ can be partitioned so that each sbuset induces an empty or a complete subgraph of __G__. In this paper we introduce the problem of determining for a surf