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Correlated Matroids

Published online by Cambridge University Press:  01 July 2008

CLIFFORD C. COCKS
CLIFFORD C. COCKS*
Affiliation:
GCHQ, Hubble Road, Cheltenham, Glos, GL51 OEX, UK (e-mail: clifford.cocks@gchq.gsi.gov.uk)
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Abstract

Semple and Welsh [5] introduced the concept of correlated matroids, which relate to conjectures by Grimmett and Winkler [2], and Pemantle [4], respectively, that the uniformly random forest and the uniformly random connected subgraph of a finite graph have the edge-negative-association property. In this paper, we extend results of Semple and Welsh, and show that the Grimmett and Winkler, and Pemantle conjectures are equivalent to statements about correlated graphic matroids. We also answer some open questions raised in [5] regarding correlated matroids, and in particular show that the 2-sum of correlated matroids is correlated.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 4 , July 2008 , pp. 511 - 518
Copyright
Copyright © Cambridge University Press 2008

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References

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