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The toroidal splitting number of the complete graphKn

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
62
Issue
1
Identifiers
DOI: 10.1016/0012-365x(86)90039-7

Abstract

Abstract The splitting number of a graph on a surface is defined, and a formula for the splitting number of the complete graph on the torus is established. The method of proof is to use Euler's generalized polyhedral formula for the lower bound, then current graphs are used to obtain the duals of splittings of K 12 s+1 and K 12 s+7 . Suitable additions are made to these duals to obtain the other cases.

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