NP-completeness and degree restricted spanning trees
The author proves among other results that the problem of deciding whether a given planar graph with maximum degree 3 has a spanning tree with node degrees 1 or 3 is NP-complete. The proof is based on a polynomial transformation from the Hamiltonian Path Variant Problem using a local replacement argument. As a corollary the author shows that it is NP-complete to decide if there is a spanning tree for such a graph with at least \(n/2+1\) leaves.
scientific article; zbMATH DE number 94345