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Paper detail

Independent sets in graphs with given minimum degree

We consider numbers and sizes of independent sets in graphs with minimum degree at least $d$, when the number $n$ of vertices is large. 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.

preprint2012arXivOpen access
Hiu-Fai LawColin McDiarmid
math.CO
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Hiu-Fai LawColin McDiarmid

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