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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

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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.

Information

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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