Path partition for graphs with special blocks

Authors:
Jun-Jie Pan;Gerard J. Chang
Affiliations:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan;Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan and Mathematics Division, National Center for Theoretical Sciences at Taipei, Old Mathematics Building, National Taiwan ...
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

The path-partition problem is to find a minimum number of vertex-disjoint paths that cover all vertices of a given graph. This paper studies the path-partition problem from an algorithmic point of view. As the Hamiltonian path problem is NP-complete for many classes of graphs, so is the path-partition problem. The main result of this paper is to present a linear-time algorithm for the path-partition problem in graphs whose blocks are complete graphs, cycles or complete bipartite graphs.