Negative association in uniform forests and connected graphs
| dc.creator | Grimmett, G. R. | |
| dc.creator | Winkler, S. N. | |
| dc.date | 2003-02-17 | |
| dc.date | 2003-02-24 | |
| dc.date.accessioned | 2026-07-07T04:55:20Z | |
| dc.date.available | 2026-07-07T04:55:20Z | |
| dc.description | 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 eighteen edges, using a certain computer algorithm which is summarised 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. | |
| dc.description | With minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0302185 | |
| dc.identifier | http://arxiv.org/abs/math/0302185 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66539 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 60C05, 05C80, 82B20 | |
| dc.title | Negative association in uniform forests and connected graphs | |
| dc.type | text |