Hamiltonian Path Reducible to Spanning Tree of Degree 2

If there an algorithm to quickly determine if a graph has a spanning tree of degree then there is an algorithm to quickly solve the Hamiltonian path problem.
- A spanning tree of degree 2 is a Hamiltonian path!
- These problems are essentially the same problem.

If there an algorithm to quickly determine if a graph has a spanning tree of degree then there is an algorithm to quickly solve the Hamiltonian path problem.