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许晓东,赵文飞,邵泽辉,梁美莲.集染色顶点和集染色边的Folkman数[J].广西科学院学报,2015,31(1):59-63. [点击复制]
- XU Xiao-dong,ZHAO Wen-fei,SHAO Ze-hui,LIANG Mei-lian.On the Set-coloring Vertex and Edge Folkman Numbers[J].Journal of Guangxi Academy of Sciences,2015,31(1):59-63. [点击复制]
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| 集染色顶点和集染色边的Folkman数 |
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许晓东1, 赵文飞2, 邵泽辉3, 梁美莲4
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| (1.广西科学院, 广西南宁 530007;2.海军航空兵工程学院, 山东烟台 264001;3.四川省高校模式识别与智能信息处理重点实验室, 成都大学信息科学与技术学院, 四川成都 610106;4.广西大学数学与信息科学学院, 广西南宁 530004) |
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| 摘要: |
| 对于给定的简单图G和正整数a1,a2,…,ak,G→(a1,a2,…,ak)rv(G→(a1,a2,…,ak)re)是指,对于V(G)(E(G))的任意k-染色,其中每个顶点(边)被用{1,…,k}的一个r-子集来染色,存在i∈{1,…,k}和一个阶为ai的完全子图,其中每个顶点(边)被一个包含颜色i的r-子集染色.本文在整数t>max{a1,a2,…,ak}的条件下,定义并研究下述集染色顶点(边) Folkman数:Fv(r)(a1,a2,…,ak;t)=min={|V(G)|:G→(a1,a2,…,ak)rv且Kt⊈G}(类似地,Fe(r)(a1,a2,…,ak;t)=min={|V(G)|:G→(a1,a2,…,ak)re且Kt⊈G}). |
| 关键词: Folkman数 集染色 Ramsey理论 |
| DOI： |
| 投稿时间：2014-11-10 |
| 基金项目:国家自然科学基金项目(批准号11361008,61309015)和广西自然科学基金项目(2011GXNSFA018142)资助。 |
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| On the Set-coloring Vertex and Edge Folkman Numbers |
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XU Xiao-dong1, ZHAO Wen-fei2, SHAO Ze-hui3, LIANG Mei-lian4
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| (1.Guangxi Academy of Sciences, Nanning, Guangxi, 530007, China;2.Naval Aeronautical Engineering Academy, Yantai, Shandong, 264001, China;3.Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, School of Information Science and Technology, Chengdu University, Chengdu, Sichuan, 610106, China;4.School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| Given a simple graph G and positive integers a1,a2,…,ak,we write G→(a1,a2,…,ak)rv (resp.G→ (a1,a2,…,ak)re) if for any k-coloring of V(G) (resp. E(G)) in which each vertex (edge) is colored with an r-subset of {1,…,k}.There exists a complete subgraph of order ai in which every vertex (resp.edge) is colored with an r-subset containing color i for some i∈{1,…,k}.In this paper, for integer t>max{a1,a2,…,ak}, the set-coloring vertex (resp.edge) Folkman number is defined and studied,Fv(r)(a1,a2,…,ak;t)=min{|V(G)|:G →(a1,a2,…,ak)rv and Kt⊈G} (resp.Fe(r)(a1,a2,…,ak;t)=min{|V(G)|:G → (a1,a2,…,ak)re and Kt⊈G}.) |
| Key words: Folkman number set coloring Ramsey theory |
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