### Abstract

A Hamiltonian walk of a connected graph is a shortest closed walk that passes through every vertex at least once, and the length of a Hamiltonian walk is the total number of edges traversed by the walk. We show that every maximal planar graph with p(≥ 3) vertices has a Hamiltonian cycle or a Hamiltonian walk of length ≤ 3(p ‐ 3)/2.

Original language | English |
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Pages (from-to) | 315-336 |

Number of pages | 22 |

Journal | Journal of Graph Theory |

Volume | 4 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1980 Jan 1 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

*4*(3), 315-336. https://doi.org/10.1002/jgt.3190040310

**An upper bound on the length of a Hamiltonian walk of a maximal planar graph.** / Asano, Takao; Nishizeki, Takao; Watanabe, Takahiro.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 4, no. 3, pp. 315-336. https://doi.org/10.1002/jgt.3190040310

}

TY - JOUR

T1 - An upper bound on the length of a Hamiltonian walk of a maximal planar graph

AU - Asano, Takao

AU - Nishizeki, Takao

AU - Watanabe, Takahiro

PY - 1980/1/1

Y1 - 1980/1/1

N2 - A Hamiltonian walk of a connected graph is a shortest closed walk that passes through every vertex at least once, and the length of a Hamiltonian walk is the total number of edges traversed by the walk. We show that every maximal planar graph with p(≥ 3) vertices has a Hamiltonian cycle or a Hamiltonian walk of length ≤ 3(p ‐ 3)/2.

AB - A Hamiltonian walk of a connected graph is a shortest closed walk that passes through every vertex at least once, and the length of a Hamiltonian walk is the total number of edges traversed by the walk. We show that every maximal planar graph with p(≥ 3) vertices has a Hamiltonian cycle or a Hamiltonian walk of length ≤ 3(p ‐ 3)/2.

UR - http://www.scopus.com/inward/record.url?scp=84986529723&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84986529723&partnerID=8YFLogxK

U2 - 10.1002/jgt.3190040310

DO - 10.1002/jgt.3190040310

M3 - Article

AN - SCOPUS:84986529723

VL - 4

SP - 315

EP - 336

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 3

ER -