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Aug 30, 2011 at 22:40 comment added Brendan McKay Available at cs.anu.edu.au/~bdm/papers/SpanningTrees1983.pdf . Incidentally Fan Chung proved the conjecture which is stated just before the Acknowledgements, but there is an error in the precise upper bound she proved. I don't know if it is resolved yet. Her paper is here: combinatorics.org/Volume_6/Abstracts/v6i1r12.html .
Aug 30, 2011 at 19:41 comment added j.c. McKay's paper is "B. McKay, Spanning trees in regular graphs, European Journal of Combinatorics 4 (1983) 149–160."
Aug 30, 2011 at 19:33 history answered Igor Rivin CC BY-SA 3.0