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The Degree Sequence of Random Graphs from Subcritical Classes†

Published online by Cambridge University Press:  01 September 2009

NICLA BERNASCONI ,
KONSTANTINOS PANAGIOTOU  and
ANGELIKA STEGER
NICLA BERNASCONI
Affiliation:
Institute of Theoretical Computer Science, ETH Zürich, Universitätsstrasse 6, CH-8092 Zürich, Switzerland (e-mail: steger@inf.ethz.ch)
KONSTANTINOS PANAGIOTOU
Affiliation:
Institute of Theoretical Computer Science, ETH Zürich, Universitätsstrasse 6, CH-8092 Zürich, Switzerland (e-mail: steger@inf.ethz.ch)
ANGELIKA STEGER
Affiliation:
Institute of Theoretical Computer Science, ETH Zürich, Universitätsstrasse 6, CH-8092 Zürich, Switzerland (e-mail: steger@inf.ethz.ch)
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Abstract

In this work we determine the expected number of vertices of degree k = k(n) in a graph with n vertices that is drawn uniformly at random from a subcritical graph class. Examples of such classes are outerplanar, series-parallel, cactus and clique graphs. Moreover, we provide exponentially small bounds for the probability that the quantities in question deviate from their expected values.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 18 , Issue 5: New Directions in Algorithms, Combinatorics and Optimization , September 2009 , pp. 647 - 681
Copyright
Copyright © Cambridge University Press 2009

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