Hamiltonian Path is Reducible Spanning Tree of Degree k for any k
Let G = (V,E) be an undirected graph. We can construct in polynomial time G’ = (V’,E’) with the property that G has a Hamiltonian path if and only if G’ has a spanning tree of degree k.
Thus, if there is a polynomial time algorithm for the spanning tree problem then there is also also for the Hamiltonian path problem.
But there is likely no such algorithm!