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Number of spanning trees: bounds from simplestructural parameters

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?

  1. What are the best known upper bounds on the number of spanning trees in a graph?

  2. 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.

Number of spanning trees: bounds from simple parameters

The Kirchhoff's theorem counts spanning trees. OK.

I have some quick questions:

  1. What are the best known upper bounds on the number of spanning trees in a graph?

  2. 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.

Number of spanning trees: bounds from structural parameters

The Kirchhoff's theorem is a classical result for counting the number of spanning trees in a graph.

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?

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user3409
user3409

Number of spanning trees: info on boundbounds from simple parameters

Dear All,

The Kirchhoff's theorem counts spanning trees. OK.

I have some quick questions:

  1. What are the best known upper bounds on the number of spanning trees in a graph?

  2. 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.

Thanks a lot...

Number of spanning trees: info on bound

Dear All,

The Kirchhoff's theorem counts spanning trees. OK.

I have some quick questions:

  1. What are the best known upper bounds on the number of spanning trees in a graph?

  2. 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.

Thanks a lot...

Number of spanning trees: bounds from simple parameters

The Kirchhoff's theorem counts spanning trees. OK.

I have some quick questions:

  1. What are the best known upper bounds on the number of spanning trees in a graph?

  2. 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.

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