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On the frequency of 3-connected subgraphs of planar graphs

Published online by Cambridge University Press:  17 April 2009

Nicholas C. Wormald
Nicholas C. Wormald
Affiliation:
Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand.
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Abstract

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The concept of dependence of subgraphs of a plane graph is defined, as a measure of how much they overlap. It is shown that if M is a 3-connected plane graph, then the number of copies of M in a plane graph which are dependent on a given copy is bounded above by a constant c (M). The number of copies of M in any n-vertex plane graph is at most nc (m).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 2 , October 1986 , pp. 309 - 317
Copyright
Copyright © Australian Mathematical Society 1986

References

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