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On Independent Sets in Graphs with Given Minimum Degree

Published online by Cambridge University Press:  16 September 2013

HIU-FAI LAW  and
COLIN McDIARMID
HIU-FAI LAW
Affiliation:
Mathematisches Seminar der Universität Hamburg, Germany (e-mail: hiufai.law@gmail.com)
COLIN McDIARMID
Affiliation:
Department of Statistics, Oxford University, UK (e-mail: cmcd@stats.ox.ac.uk)
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Abstract

We consider numbers and sizes of independent sets in graphs with minimum degree at least d. In particular, we investigate which of these graphs yield the maximum numbers of independent sets of different sizes, and which yield the largest random independent sets. We establish a strengthened form of a conjecture of Galvin concerning the first of these topics.

Keywords

Primary 05C35Secondary 05C6905C07
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 6 , November 2013 , pp. 874 - 884
Copyright
Copyright © Cambridge University Press 2013 

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