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- W2949117595 abstract "Abstract 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 vertices, or having nine vertices and no more than 18 edges, using a certain computer algorithm which is summarized in this paper. Negative association is known already to be valid for a uniform spanning tree. The three cases of uniform forest, uniform spanning tree, and uniform connected subgraph are special cases of a more general conjecture arising from the random‐cluster model of statistical mechanics. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004" @default.
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- W2949117595 date "2004-04-29" @default.
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- W2949117595 title "Negative association in uniform forests and connected graphs" @default.
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- W2949117595 doi "https://doi.org/10.1002/rsa.20012" @default.
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