TY - GEN

T1 - A neural network parallel algorithm for Ramsey numbers

AU - Tsuchiya, K.

AU - Takefuji, Y.

N1 - Publisher Copyright:
© 1992 IEEE.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 1992

Y1 - 1992

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.

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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.

T2 - 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992

Y2 - 7 October 1992 through 10 October 1992

ER -