The Kirchhoff's theorem countsis a classical result for counting the number of spanning trees. OK in a graph.
I have some quick questions:However, what are the best known upper bounds on the number of spanning trees in a graph in terms of structural parameters (e.g., number of vertices, degrees, etc.) instead of algebraic quantities?
What are the best known upper bounds on the number of spanning trees in a graph?
I did not find much information about lower bounds. Is it because the problem is trivial, or simply not interesting? I do not know why it is trivial, in case, but this is my naive answer.