Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs

Authors:
Ruo-Wei Hung;Maw-Shang Chang
Affiliations:
Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi, Taiwan;Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi, Taiwan
Venue:
Theoretical Computer Science
Year:
2005

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Abstract

A Hamiltonian path of a graph G is a simple path that contains each vertex of G exactly once. A Hamiltonian cycle of a graph is a simple cycle with the same property. The Hamiltonian path (resp. cycle) problem involves testing whether a Hamiltonian path (resp. cycle) exists in a graph. The 1HP (resp. 2HP) problem is to determine whether a graph has a Hamiltonian path starting from a specified vertex (resp. starting from a specified vertex and ending at the other specified vertex). The Hamiltonian problems include the Hamiltonian path, Hamiltonian cycle, 1HP, and 2HP problems. A graph is a distance-hereditary graph if each pair of vertices is equidistant in every connected induced subgraph containing them. In this paper, we present a unified approach to solving the Hamiltonian problems on distance-hereditary graphs in linear time.