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On a Correlation Inequality of Farr

Published online by Cambridge University Press:  12 September 2008

Colin McDiarmid
Colin McDiarmid
Affiliation:
Department of Statistics, Oxford University
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Abstract

Suppose that each vertex of a graph independently chooses a colour uniformly from the set {1, …, k}; and let Si be the random set of vertices coloured i. Farr shows that the probability that each set Si is stable (so that the colouring is proper) is at most the product of the k probabilities that the sets Si separately are stable. We give here a simple proof of an extension of this result.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 2 , June 1992 , pp. 157 - 160
Copyright
Copyright © Cambridge University Press 1992

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References

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