### Abstract

Graph theory is applied in wide area of computer science, including artificial intelligence and operations research. Indeed, graphs are used as models for practical problems. Graph theory, therefore, has potentiality for being useful tools in actual world. In this paper, a computational problem in graph theory, called Eulerian recurrent length, is introduced. The problem asks, for an Eulerian graph and a positive integer, whether there exists an Eulerian circuit of the Eulerian graph such that the length of a shortest subcycle in the Eulerian circuit is greater than or equal to the positive integer. The maximum length of shortest subcycles in Eulerian circuits of an Eulerian graph is referred to as the Eulerian recurrent length of the Eulerian graph by the author. The NP-completeness of the Eulerian recurrent length problem is proved even if each instance is restricted to a pair of a 4-regular graph and any constant greater than 330.

Original language | English |
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Title of host publication | Proceedings - 2014 4th International Conference on Artificial Intelligence with Applications in Engineering and Technology, ICAIET 2014 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 155-159 |

Number of pages | 5 |

ISBN (Print) | 9781479979103 |

DOIs | |

Publication status | Published - Dec 9 2015 |

Event | 4th International Conference on Artificial Intelligence with Applications in Engineering and Technology, ICAIET 2014 - Kota Kinabalu, Sabah, Malaysia Duration: Dec 2 2014 → Dec 5 2014 |

### Other

Other | 4th International Conference on Artificial Intelligence with Applications in Engineering and Technology, ICAIET 2014 |
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Country | Malaysia |

City | Kota Kinabalu, Sabah |

Period | 12/2/14 → 12/5/14 |

### Fingerprint

### Keywords

- Eulerian circuit
- Eulerian graph
- Graph theory
- NP-completeness

### ASJC Scopus subject areas

- Computer Science Applications
- Engineering (miscellaneous)
- Artificial Intelligence

### Cite this

*Proceedings - 2014 4th International Conference on Artificial Intelligence with Applications in Engineering and Technology, ICAIET 2014*(pp. 155-159). [7351828] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICAIET.2014.34

**The NP-completeness of Eulerian Recurrent Length for 4-regular Eulerian Graphs.** / Jinbo, Shuji.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 2014 4th International Conference on Artificial Intelligence with Applications in Engineering and Technology, ICAIET 2014.*, 7351828, Institute of Electrical and Electronics Engineers Inc., pp. 155-159, 4th International Conference on Artificial Intelligence with Applications in Engineering and Technology, ICAIET 2014, Kota Kinabalu, Sabah, Malaysia, 12/2/14. https://doi.org/10.1109/ICAIET.2014.34

}

TY - GEN

T1 - The NP-completeness of Eulerian Recurrent Length for 4-regular Eulerian Graphs

AU - Jinbo, Shuji

PY - 2015/12/9

Y1 - 2015/12/9

N2 - Graph theory is applied in wide area of computer science, including artificial intelligence and operations research. Indeed, graphs are used as models for practical problems. Graph theory, therefore, has potentiality for being useful tools in actual world. In this paper, a computational problem in graph theory, called Eulerian recurrent length, is introduced. The problem asks, for an Eulerian graph and a positive integer, whether there exists an Eulerian circuit of the Eulerian graph such that the length of a shortest subcycle in the Eulerian circuit is greater than or equal to the positive integer. The maximum length of shortest subcycles in Eulerian circuits of an Eulerian graph is referred to as the Eulerian recurrent length of the Eulerian graph by the author. The NP-completeness of the Eulerian recurrent length problem is proved even if each instance is restricted to a pair of a 4-regular graph and any constant greater than 330.

AB - Graph theory is applied in wide area of computer science, including artificial intelligence and operations research. Indeed, graphs are used as models for practical problems. Graph theory, therefore, has potentiality for being useful tools in actual world. In this paper, a computational problem in graph theory, called Eulerian recurrent length, is introduced. The problem asks, for an Eulerian graph and a positive integer, whether there exists an Eulerian circuit of the Eulerian graph such that the length of a shortest subcycle in the Eulerian circuit is greater than or equal to the positive integer. The maximum length of shortest subcycles in Eulerian circuits of an Eulerian graph is referred to as the Eulerian recurrent length of the Eulerian graph by the author. The NP-completeness of the Eulerian recurrent length problem is proved even if each instance is restricted to a pair of a 4-regular graph and any constant greater than 330.

KW - Eulerian circuit

KW - Eulerian graph

KW - Graph theory

KW - NP-completeness

UR - http://www.scopus.com/inward/record.url?scp=84969674496&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84969674496&partnerID=8YFLogxK

U2 - 10.1109/ICAIET.2014.34

DO - 10.1109/ICAIET.2014.34

M3 - Conference contribution

AN - SCOPUS:84969674496

SN - 9781479979103

SP - 155

EP - 159

BT - Proceedings - 2014 4th International Conference on Artificial Intelligence with Applications in Engineering and Technology, ICAIET 2014

PB - Institute of Electrical and Electronics Engineers Inc.

ER -