15
votes
1answer
564 views

Paul Erdős: Determine or estimate the number of maximal triangle-free graphs on n vertices

Among the collections of the open problems of Paul Erdős on the website of Professor Fan Chung, there is one called "number of triangle-free graphs". ...
8
votes
1answer
262 views

Maximal class of simple graphs of order $n$ with mutually distinct numbers of spanning trees

This problem in some ways related to this post. Let $A_n$ be the set of all integers $x$ such that there exist a connected simple graph of order $n$ having precisely $x$ spanning trees. Study the ...
15
votes
2answers
760 views

Minimal graphs with a prescribed number of spanning trees

As its long ago since Erdős died and mathoverflow is the second best alternative to him (for discussing personal problems), I'd like to start a fruitful discussion about the following problem ...