Degree-preserving spanning trees on strongly chordal graphs and directed path graphs

Suppose G is a connected graph and T a spanning tree of G. A vertex v ∈ V (G) is said to be a degree-preserving vertex if its degree in T is the same as in G. The degree-preserving spanning tree problem is to find a spanning tree T of a connected graph G such that the number of degreepreserving vertices is maximum. The purpose of this paper is to give an O(mα(m,n))-time algorithm for the degree-preserving spanning tree problem on strongly chordal graphs and an O(m+ n)time algorithm on directed path graphs, where α is the inverse of Ackermann’s function.