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Asymptotic properties of rooted 3-connected maps on surfaces

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

Edward A. Bender ,
Zhicheng Gao ,
L. Bruce Richmond  and
Nicholas C. Wormald
Edward A. Bender
Affiliation:
Center for Communications Research4350 Executive Drive San Diego, CA 92121, USA
Zhicheng Gao
Affiliation:
Department of Combinatorics and OptimizationUniversity of Waterloo Waterloo, Ontario N2L3G1, Canada
L. Bruce Richmond
Affiliation:
Department of Combinatorics and OptimizationUniversity of WaterlooWaterloo, Ontario N2L3G1, Canada
Nicholas C. Wormald
Affiliation:
Department of MathematicsUniversity of MelbourneParkville, VIC 3052Australia e-mail: [email protected]
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Abstract

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In this paper we obtain asymptotics for the number of rooted 3-connected maps on an arbitrary surface and use them to prove that almost all rooted 3-connected maps on any fixed surface have large edge-width and large face-width. It then follows from the result of Roberston and Vitray [10] that almost all rooted 3-connected maps on any fixed surface are minimum genus embeddings and their underlying graphs are uniquely embeddable on the surface.

MSC classification

Secondary: 05C10: Planar graphs; geometric and topological aspects of graph theory 05C30: Enumeration in graph theory 05C15: Coloring of graphs and hypergraphs
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 1 , February 1996 , pp. 31 - 41
Copyright
Copyright © Australian Mathematical Society 1996

References

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