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Planar maps with prescribed types of vertices and faces

Published online by Cambridge University Press:  26 February 2010

Branko Grünbaum
Branko Grünbaum
Affiliation:
University of Washington
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Extract

For a 3-connected graph G imbedded in the plane let νk(G) denote the number of k-valent vertices, and let pk(G) denote the number of k-gonal faces (countries) of the map defined by G. (We consider only graphs without loops or multiple edges; hence, νk(G) and pk(G) are defined only for k ≥ 3.) It is a wellknown consequence of Euler's formula that

Type
Research Article
Information
Mathematika , Volume 16 , Issue 1 , June 1969 , pp. 28 - 36
Copyright
Copyright © University College London 1969

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References

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