Negative association in uniform forests and connected graphs

@article{Grimmett2004NegativeAI,
  title={Negative association in uniform forests and connected graphs},
  author={Geoffrey R. Grimmett and S. N. Winkler},
  journal={Random Struct. Algorithms},
  year={2004},
  volume={24},
  pages={444-460}
}
G. R. Grimmett and S. N. Winkler Abstra t. We consider three probability measures on subsets of edges of a given finite graph G, namely those which govern, respectively, a uniform forest, a uniform spanning tree, and a uniform connected subgraph. A conjecture concerning the negative association of two edges is reviewed for a uniform forest, and a related conjecture is posed for a uniform connected subgraph. The former conjecture is verified numerically for all graphs G having eight or fewer… CONTINUE READING
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