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Some Results on k-maps

Published online by Cambridge University Press:  03 November 2016

B. L. Meek
B. L. Meek*
Affiliation:
Dept. of Mathematics, Queen Elizabeth College, London
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Extract

For convenience we shall repeat here the definition by Hawkins, Hill, Reeve and Tyrrell (1, hereafter referred to as HHRT) of a k-map:

Definition

A map is called a k-map if each of the following conditions is satisfied:

  1. (i) It is a map on a sphere;

  2. (ii) Each face is a connected region whose boundary is a simple closed curve;

  3. (iii) Each vertex has at least three edges incident with it and each face has at least three edges on its boundary;

  4. (iv) Each face has exactly k edges, and therefore exactly k vertices.

Type
Research Article
Information
The Mathematical Gazette , Volume 52 , Issue 379 , February 1968 , pp. 33 - 42
Copyright
Copyright © Mathematical Association 1968

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References

[1] Hawkins, A. F., Hill, A. C., Reeve, J. E., and Tyrrell, J. A.: On Certain Polyhedra (Math. Gazette, 50, 140, May 1966).CrossRefGoogle Scholar
[2] Brown, W. G.: Enumeration of triangular dissections of the disk (Proc. London Math. Soc. 14, 746, 1964).CrossRefGoogle Scholar
[3] Brown, W. G.: Enumeration of quadrangular dissections of the disk (Can. J. Math. 17, 302, 1965).CrossRefGoogle Scholar
[4] Garreau, G. A.: The Problem Bureau and some of its problems (Math. Gazette, 51, 1, February 1967).Google Scholar