### Abstract

A hamiltonian walk of a graph is a shortest closed walk that passes through every vertex at least once, and the length is the total number of traversed edges. The hamiltonian walk problem in which one would like to find a hamiltonian walk of a given graph is NP-complete. The problem is a generalized hamiltonian cycle problem and is a special case of the traveling salesman problem. Employing the techniques of divide-and-conquer and augmentation, we present an approximation algorithm for the problem on maximal planar graphs. The algorithm finds, in O(p^{2}) time, a closed spanning walk of a given arbitrary maximal planar graph, and the length of the obtained walk is at most 3 2(p - 3) if the graph has p (≥ 9) vertices. Hence the worst-case bound is 3 2.

Original language | English |
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Pages (from-to) | 211-222 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 5 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1983 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Applied Mathematics*,

*5*(2), 211-222. https://doi.org/10.1016/0166-218X(83)90042-2

**An approximation algorithm for the hamiltonian walk problem on maximal planar graphs.** / Nishizeki, Takao; Asano, Takao; Watanabe, Takahiro.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 5, no. 2, pp. 211-222. https://doi.org/10.1016/0166-218X(83)90042-2

}

TY - JOUR

T1 - An approximation algorithm for the hamiltonian walk problem on maximal planar graphs

AU - Nishizeki, Takao

AU - Asano, Takao

AU - Watanabe, Takahiro

PY - 1983

Y1 - 1983

N2 - A hamiltonian walk of a graph is a shortest closed walk that passes through every vertex at least once, and the length is the total number of traversed edges. The hamiltonian walk problem in which one would like to find a hamiltonian walk of a given graph is NP-complete. The problem is a generalized hamiltonian cycle problem and is a special case of the traveling salesman problem. Employing the techniques of divide-and-conquer and augmentation, we present an approximation algorithm for the problem on maximal planar graphs. The algorithm finds, in O(p2) time, a closed spanning walk of a given arbitrary maximal planar graph, and the length of the obtained walk is at most 3 2(p - 3) if the graph has p (≥ 9) vertices. Hence the worst-case bound is 3 2.

AB - A hamiltonian walk of a graph is a shortest closed walk that passes through every vertex at least once, and the length is the total number of traversed edges. The hamiltonian walk problem in which one would like to find a hamiltonian walk of a given graph is NP-complete. The problem is a generalized hamiltonian cycle problem and is a special case of the traveling salesman problem. Employing the techniques of divide-and-conquer and augmentation, we present an approximation algorithm for the problem on maximal planar graphs. The algorithm finds, in O(p2) time, a closed spanning walk of a given arbitrary maximal planar graph, and the length of the obtained walk is at most 3 2(p - 3) if the graph has p (≥ 9) vertices. Hence the worst-case bound is 3 2.

UR - http://www.scopus.com/inward/record.url?scp=0020707585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020707585&partnerID=8YFLogxK

U2 - 10.1016/0166-218X(83)90042-2

DO - 10.1016/0166-218X(83)90042-2

M3 - Article

VL - 5

SP - 211

EP - 222

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 2

ER -