On a Correlation Inequality of Farr
- 1 June 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 1 (2) , 157-160
- https://doi.org/10.1017/s096354830000016x
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.Keywords
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