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The random division of faces in a planar graph

Published online by Cambridge University Press:  01 July 2016

Richard Cowan  and
Simone Chen
Richard Cowan
Affiliation:
The University of Hong Kong
Simone Chen
Affiliation:
The University of Hong Kong
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Extract

Consider a connected planar graph. A bounded face is said to be of type k, or is called a k-face, if the boundary of that face contains k edges. Under various natural rules for randomly dividing bounded faces by the addition of new edges, we investigate the limiting distribution of face type as the number of divisions increases.

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 331
Copyright
Copyright © Applied Probability Trust 1996 

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References

Cowan, R. (1989) The division of space and the Poisson distribution. Adv. Appl. Prob. 21, 233–234.Google Scholar
Cowan, R. and Morris, V. B. (1988) Division rules for polygonal cells. J. Theor. Biol. 131, 33–42.CrossRefGoogle ScholarPubMed