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许晓东,罗海鹏,苏文龙,吴康.关于顶点Folkman数的新不等式[J].广西科学,2006,13(4):249-252. [点击复制]
- XU Xiao-dong,LUO Hai-peng,SU Wen-long,WU Kang.New Inequalities on Vertex Folkman Numbers[J].Guangxi Sciences,2006,13(4):249-252. [点击复制]
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| 关于顶点Folkman数的新不等式 |
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许晓东1, 罗海鹏1, 苏文龙2, 吴康3
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| (1.广西科学院, 广西南宁 530007;2.梧州学院, 广西梧州 543002;3.华南师范大学数学科学学院, 广东广州 510631) |
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| 摘要: |
| 对于无向简单图G及正整数a1,…,ak,记G→(a1,…,ak)v当且仅当对于图G的任意一种顶点k染色,一定对某个i∈{1,…,k}存在顶点全染着颜色i的完全子图Kai.对于p>max{a1,…,ak},定义Fv(a1,…,ak;p)=min{V(G):G→(a1,…,ak)v,Kp⊄G}为顶点Folkman数.证明关于顶点Folkman数Fv(k,k;k+1)的新的迭代不等式,并推广Kolev和Nenov的一个关于多色顶点Folkman数的不等式. |
| 关键词: 顶点Folkman数 上界 染色 |
| DOI： |
| 投稿时间：2006-06-06 |
| 基金项目:Partially Supported by the National Natural Science Fund of China (60563008). |
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| New Inequalities on 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.School of Mathematics, South China Normal University, Guangzhou, Guangdong, 510631, China) |
| Abstract: |
| For an undirected,simple graph G,and positive integers a1,…,ak,we write G→(a1,…,ak)v if and only if for every vertex k-coloring of G,there exists a monochromatic Kai,for some color i∈{1,…,k}.The vertex Folkman number is defined as Fv(a1,…,ak;p)=min{|V(G)|:G→(a1,…,ak)v,Kp⊄G}for p>max{a1,…,ak}.In this paper,new recurrent inequalities on vertex Folkman numbers Fv(k,k;k+1) are proved.We also generalize an inequality of Kolev and Nenov on multicolor Folkman numbers. |
| Key words: vertex Folkman number upper bound coloring |
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