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The Maximum Degree of Series-Parallel Graphs

Published online by Cambridge University Press:  31 May 2011

MICHAEL DRMOTA ,
OMER GIMÉNEZ  and
MARC NOY
MICHAEL DRMOTA
Affiliation:
Institute of Discrete Mathematics and Geometry, Technische Universität Wien, Wiedner Hauptstrasse 8–10, A–1040 Wien, Austria (e-mail: michael.drmota@tuwien.ac.at)
OMER GIMÉNEZ
Affiliation:
Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Jordi Girona 1–3, 08034 Barcelona, Spain (e-mail: omer.gimenez@upc.edu)
MARC NOY
Affiliation:
Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1–3, 08034 Barcelona, Spain (e-mail: marc.noy@upc.edu)
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Abstract

We prove that the maximum degree Δn of a random series-parallel graph with n vertices satisfies Δn/logn → c in probability, and Δn ~ c logn for a computable constant c > 0. The same kind of result holds for 2-connected series-parallel graphs, for outerplanar graphs, and for 2-connected outerplanar graphs.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 4 , July 2011 , pp. 529 - 570
Copyright
Copyright © Cambridge University Press 2011

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