A Linear-Time Algorithm for the Terminal Path Cover Problem in Trees

Abstract

Let G = (V,E) be a graph with vertex set V and edge set E and let T be a subset of V. A terminal path cover PC of G with respect to T is a set of pairwise vertex-disjoint paths of G which cover the vertices of G such that all vertices in T are end vertices of paths in PC. The terminal path cover problem is to find a terminal path cover of G of minimum cardinality with respect to T . The path cover problem is a special case of the terminal path cover problem with T be empty. In this paper, we show that the terminal path cover problem on trees can be solved in linear time.