### Abstract

A neural network parallel algorithm for finding Ramsey numbers in two-coloring is described. The Ramsey number R(r,b) is given by the smallest value of N, where all edges of a complete graph of (N-1) vertices are colored either red or blue, and red-colored and blue-colored subgraphs should not form any complete subgraph of r vertices and b vertices, respectively. A superimposed red-colored and blue-colored subgraph is called a Ramsey graph. The parallel algorithm, which is based on the hysteresis McCulloch-Pitts neural network, found five Ramsey numbers successfully. The neural network requires n(n-1) neurons for a Ramsey number of an n-vertex complete graph. The simulation result for the algorithm is so promising that it may be possible to find unknown Ramsey numbers.

Original language | English |
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Title of host publication | Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1166-1171 |

Number of pages | 6 |

ISBN (Electronic) | 0780308093, 9780780308091 |

DOIs | |

Publication status | Published - 1992 Jan 1 |

Externally published | Yes |

Event | 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992 - Rostov-on-Don, Russian Federation Duration: 1992 Oct 7 → 1992 Oct 10 |

### Publication series

Name | Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992 |
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### Conference

Conference | 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992 |
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Country | Russian Federation |

City | Rostov-on-Don |

Period | 92/10/7 → 92/10/10 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Science Applications
- Information Systems

### Cite this

*Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992*(pp. 1166-1171). [268617] (Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/RNNS.1992.268617

**A neural network parallel algorithm for Ramsey numbers.** / Tsuchiya, K.; Takefuji, Yoshiyasu.

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

*Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992.*, 268617, Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992, Institute of Electrical and Electronics Engineers Inc., pp. 1166-1171, 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992, Rostov-on-Don, Russian Federation, 92/10/7. https://doi.org/10.1109/RNNS.1992.268617

}

TY - GEN

T1 - A neural network parallel algorithm for Ramsey numbers

AU - Tsuchiya, K.

AU - Takefuji, Yoshiyasu

PY - 1992/1/1

Y1 - 1992/1/1

N2 - A neural network parallel algorithm for finding Ramsey numbers in two-coloring is described. The Ramsey number R(r,b) is given by the smallest value of N, where all edges of a complete graph of (N-1) vertices are colored either red or blue, and red-colored and blue-colored subgraphs should not form any complete subgraph of r vertices and b vertices, respectively. A superimposed red-colored and blue-colored subgraph is called a Ramsey graph. The parallel algorithm, which is based on the hysteresis McCulloch-Pitts neural network, found five Ramsey numbers successfully. The neural network requires n(n-1) neurons for a Ramsey number of an n-vertex complete graph. The simulation result for the algorithm is so promising that it may be possible to find unknown Ramsey numbers.

AB - A neural network parallel algorithm for finding Ramsey numbers in two-coloring is described. The Ramsey number R(r,b) is given by the smallest value of N, where all edges of a complete graph of (N-1) vertices are colored either red or blue, and red-colored and blue-colored subgraphs should not form any complete subgraph of r vertices and b vertices, respectively. A superimposed red-colored and blue-colored subgraph is called a Ramsey graph. The parallel algorithm, which is based on the hysteresis McCulloch-Pitts neural network, found five Ramsey numbers successfully. The neural network requires n(n-1) neurons for a Ramsey number of an n-vertex complete graph. The simulation result for the algorithm is so promising that it may be possible to find unknown Ramsey numbers.

UR - http://www.scopus.com/inward/record.url?scp=85067354691&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067354691&partnerID=8YFLogxK

U2 - 10.1109/RNNS.1992.268617

DO - 10.1109/RNNS.1992.268617

M3 - Conference contribution

AN - SCOPUS:85067354691

T3 - Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992

SP - 1166

EP - 1171

BT - Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992

PB - Institute of Electrical and Electronics Engineers Inc.

ER -