Some properties of Ramsey numbers |
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| Authors: | Zhongfu Zhang Linzhong Liu Jinwen Li Enmin Song |
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| Institution: | Institute of Applied Mathematics, Lanzhou Railway Institute, Lanzhou Gansu, 730070, P.R. China;Department of Traffic and Transportation Engineering Lanzhou Railway Institute, Lanzhou Gansu, 730070, P.R. China;Institute of Applied Mathematics, Lanzhou Railway Institute, Lanzhou Gansu, 730070, P.R. China;Department of Computer, Huazhong Polytechnical University, Wuhan 430074, P.R. China |
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| Abstract: | In this paper, some properties of Ramsey numbers are studied, and the following results are presented. - 1. (1) For any positive integers k1, k2, …, km l1, l2, …, lm (m> 1), we have .
- 2. (2) For any positive integers k1, k2, …, km, l1, l2, …, ln , we have . Based on the known results of Ramsey numbers, some results of upper bounds and lower bounds of Ramsey numbers can be directly derived by those properties.
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| Keywords: | Ramsey number Clique Independent set Ingenuity graph |
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