Finding a minimum path cover of a distance-hereditary graph in polynomial time

  • Authors:

  • Ruo-Wei Hung;Maw-Shang Chang

  • Affiliations:

  • Department of Computer Science and Information Engineering, Chaoyang University of Technology, Wufong, Taichung 413, Taiwan;Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi 621, Taiwan

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2007

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Abstract

A path cover of a graph G=(V,E) is a set of pairwise vertex-disjoint paths such that the disjoint union of the vertices of these paths equals the vertex set V of G. The path cover problem is, given a graph, to find a path cover having the minimum number of paths. The path cover problem contains the Hamiltonian path problem as a special case since finding a path cover, consisting of a single path, corresponds directly to the Hamiltonian path problem. A graph is a distance-hereditary graph if each pair of vertices is equidistant in every connected induced subgraph containing them. The complexity of the path cover problem on distance-hereditary graphs has remained unknown. In this paper, we propose the first polynomial-time algorithm, which runs in O(|V|^9) time, to solve the path cover problem on distance-hereditary graphs.