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| 9个经典Ramsey数R(3,t)的新下界 | |
| 引用本文： | 陈红,吴康,许晓东,苏文龙,梁文忠.9个经典Ramsey数R(3,t)的新下界[J].数学杂志,2011,31(3):582-586. |
| 作者姓名： | 陈红 吴康 许晓东 苏文龙 梁文忠 |
| 作者单位： | 1. 梧州学院数理系,广西梧州,543002 2. 华南师范大学数学科学学院,广东广州,510631 3. 广西科学院,广西南宁,530003 |
| 基金项目： | 国家自然科学基金资助项目，广东省自然科学基金，广西自然科学基金，广西教育厅科研项目，梧州学院科研项目 |
| 摘 要： | 本文研究了经典Ramsey数R(3,t)的下界问题.利用素数阶循环图的性质改进一般阶循环图团数的计算方法,获得了9个经典Ramsey数R(3,t)的新下界:R(3,29)≥183,R(3,30)≥189,R(3,32)≥213,R(3,33)≥218,R(3,34)≥226,R(3,35)≥231,R(3,36)≥239,R(3,37)≥244,R(3,38)≥256,其中前三个结果分别改进了迄今已知的最好的下界,后6个结果是本文首次报道的. |
| 关 键 词： | Ramsey数 下界 循环图 |
NEW LOWER BOUNDS FOR 9 CLASSICAL RAMSEY NUMBERS |
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| CHEN Hong,WU Kang,XU Xiao-dong,SU Wen-long,LIANG Wen-zhong.NEW LOWER BOUNDS FOR 9 CLASSICAL RAMSEY NUMBERS[J].Journal of Mathematics,2011,31(3):582-586. | |
| Authors: | CHEN Hong WU Kang XU Xiao-dong SU Wen-long LIANG Wen-zhong |
| Institution: | 1(1.Dept of Phy. and Math.,Wuzhou University,Wuzhou 543002,China)(2.School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China)(3.Guangxi Academy of Sciences,Nanning 530003,China) |
| Abstract: | In the paper,we study the lower bounds for classical Ramsey number R(3,t).By using the property of cyclic graphs of prime order,the methods of computing clique numbers for cyclic graphs of general order are improved.New lower bounds for 9 classical Ramsey numbers are obtained: R(3,29) ≥ 183,R(3,30) ≥ 189,R(3,32) ≥ 213,R(3,33) ≥ 218,R(3,34) ≥ 226,R(3,35) ≥ 231,R(3,36) ≥ 239,R(3,37) ≥ 244,R(3,38) ≥ 256,where the first 3 results improve their corresponding best known lower bounds and the remaining 6 results are first reported in this article. |
| Keywords: | Ramsey mummers lower bound cyclic graph |
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