| 引用本文： |
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许晓东,罗海鹏,苏文龙,吴康.顶点Folkman数的上界[J].广西科学,2008,15(3):211-215. [点击复制]
- XU Xiao-dong,LUO Hai-peng,SU Wen-long,WU Kang.On the Upper Bounds for Vertex Folkman Numbers[J].Guangxi Sciences,2008,15(3):211-215. [点击复制]
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| 摘要: |
| 证明关于顶点Folkman数上界的新不等式.特别地,用构造性方法证明:对于任意满足0 < r < 1/2log23-3/4的实数r,存在N(r)>0和c(r)>0使得Fv(k,k;k+1)≤ c(r)(k-1)1/4log2(k-1)-r对任意的k ≥ N(r)成立,其中N(r)和c(r)都是只依赖于r的常数. |
| 关键词: 顶点Folkman数 上界 合成图 |
| DOI： |
| 投稿时间：2008-03-06 |
| 基金项目:Partially Supported by the National Natural Science Fund of China(60563008);the Basic Research Fund of Guangxi Academy of Sciences(080414) |
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| On the Upper Bounds for Vertex Folkman Numbers |
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XU Xiao-dong1, LUO Hai-peng1, SU Wen-long2, WU Kang3
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| (1.Guangxi Academy of Sciences, Nanning, Guangxi, 530007, China;2.Wuzhou University, Wuzhou, Guangxi, 543002, China;3.South China Normal University, Guangzhou, Guangdong, 510631, China) |
| Abstract: |
| Some new inequalities on the upper bounds for vertex Folkman numbers are proven in this paper.In particular, we prove the following result by constructive method:for any real number r that satisfies 0 < r < 1/2log23-3/4, there are N (r)>0 and c (r)>0 such that Fv (k, k;k+1)≤ c (r) (k-1)1/4log2 (k-1)-r for any k ≥ N (r), in which both N (r)and c (r)are constants only depending on r. |
| Key words: vertex Folkman number upper bound composition |
