Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-19T05:41:05.856Z Has data issue: false hasContentIssue false
  • English
  • Français

Toroidal maps with prescribed types of vertices and faces

Published online by Cambridge University Press:  26 February 2010

D. Barnette ,
E. Jucovic  and
M. Trenkler
D. Barnette
Affiliation:
University of California, Davis, California, U.S.A.
E. Jucovic
Affiliation:
P. J. Safarik University, Kosice, California, U.S.A.
Get access

Extract

Let a 3-connected graph G be embedded in an orientable surface of genus g in such a way that the connected components of its complement in the surface are topological discs. We denote by vk(G) the number of k-valent vertices of G and by pk(G) the number of k-gonal faces of the map defined by the embedded graph. For the numbers vk(G) and pk(G), it follows from Euler's formula that

Type
Research Article
Information
Mathematika , Volume 18 , Issue 1 , June 1971 , pp. 82 - 90
Copyright
Copyright © University College London 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Grünbaum, B., Convex polytopes (Wiley, New York, 1967).Google Scholar
2.Grünbaum, B., “Planar maps with prescribed types of vertices and faces”, Mathematika, 16 (1969), 28–36.CrossRefGoogle Scholar
3.Grünbaum, B., “Polytopes, graphs, and complexes”, Bull. Amer. Math. Soc. (to appear).Google Scholar
4.Grünbaum, B. and Shephard, G. C., “Convex polytopes”, Bull. London Math. Soc, 1 (1969), 257–300.CrossRefGoogle Scholar