A Linear-Time Algorithm for Finding a Spanning Tree with Non-Terminal Set V_NT on Interval Graphs

Abstract

Given a graph G=(V,E) where V and E are a vertex and an edge set, respectively, specified with a subset V_NT of vertices called a non-terminal set, the spanning tree with non-terminal set V_NT is a connected and acyclic spanning subgraph of G that contains all the vertices of V where each vertex in a non-terminal set is not a leaf. The complexity of finding a spanning tree with non-terminal set V_NT on general graphs where each edge has the weight of one is known to be NP-hard. In this paper, we show that if G is an interval graph then finding a spanning tree with a non-terminal set V_NT of G is linearly-solvable when each edge has the weight of one.