There are several upper and lower bounds for $m_G[2,n]$ (the number of Laplacian eigenvalues of a graph $G$ with $n$ vertices in the interval $[2,n]$).
I want to know whether there exists any bound if we replace $k\in \mathbb{N}$ instead of $2$.
Especially when the interval is $[3,n]$?
At least is there any bound if the graph is a tree or other special cases?
