A Polynomial-Time Algorithm for Finding a Spanning Tree with Non-Terminal Set V-NT on Circular-Arc Graphs

Given a graph G = (V, E), where V and E are vertex and edge sets of G, and a subset V-NT of vertices called a non-terminal set, a spanning tree with a non-terminal set V-NT, denoted by STNT, is a connected and acyclic spanning subgraph of G that contains all vertices of V where each vertex in a non-terminal set is not a leaf. On general graphs, the problem of finding an STNT of G is known to be NP-hard. In this paper, we show that if G is a circular-arc graph then finding an STNT of G is polynomially solvable with respect to the number of vertices.