A new connection between second moments and pairwise negative correlation proves the p-NC property for minimal spanning trees and shows that the second moment of degrees in uniform spanning trees on finite connected regular graphs is at most 6.
Shortest connection networks and some generalizations.The Bell System Technical Journal, 36(6):1389–1401, 1957
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From second moments to pairwise negative correlation: applications to minimal and uniform spanning trees
A new connection between second moments and pairwise negative correlation proves the p-NC property for minimal spanning trees and shows that the second moment of degrees in uniform spanning trees on finite connected regular graphs is at most 6.