The $k$-bounded spanning tree problem is where you have an undirected graph $G(V,E)$ and you have to decide whether or not it has a spanning tree such that each vertex has a degree of at most $k$.
I realize that for the case $k=2$, this is the Hamiltonian path problem. However I'm having trouble with cases where $k>2$. I tried thinking about it in the sense that you can add more nodes onto an existing spanning tree where $k=2$ and maybe since the base is NP complete, adding things on will make it NP-complete as well, but that doesn't seem right. I'm self-studying CS and am having trouble with theory, so any help will be appreciated!