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Plane Cubic Graphs with Prescribed Face Areas

Published online by Cambridge University Press:  12 September 2008

Carsten Thomassen
Carsten Thomassen
Affiliation:
Mathematical Institute, Technical University of Denmark, DK-2800 Lyngby, Denmark
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Abstract

If G is a plane, cubic graph, then G has a drawing such that each edge is a straight line segment and each bounded face has any prescribed area. The special case where all areas are the same proves a conjecture of G. Ringel, who gave an example of a plane triangulation that cannot be drawn in this way.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 4 , December 1992 , pp. 371 - 381
Copyright
Copyright © Cambridge University Press 1992

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