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| 关于图的瑕边着色 | |
| 引用本文： | 姚明,姚兵,谢建民,张忠辅.关于图的瑕边着色[J].甘肃高师学报,2009,14(2). |
| 作者姓名： | 姚明 姚兵 谢建民 张忠辅 |
| 作者单位： | 1. 兰州石化职业技术学院,信息处理与控制工程系,甘肃兰州,730060 2. 西北师范大学,数学与信息科学学院,甘肃兰州,730070 3. 兰州城市学院,数学学院,甘肃兰州,730070 |
| 摘 要： | 图G=(V,E)的一个(λ,β)-瑕k-边着色是一个从E到{1,2,…,k}的映射,且存在一个最小整数β≥1,对每一个色j∈{1,2,…,β},至少存在一个顶点uj∈V(G)使得顶点uj关联着有色的j条边;对每一个色l∈{β+1,…,k},没有两条相邻边着有色l.图G的(λ,β)-瑕色数被表示为χ(λ,β)(G),它是一个最小的整数,使对整数k≥χ(λ,(β)G),图G总有一个(λ,β)-瑕k-边着色.在这篇文章中,我们证得χ(λ,1)(G)+λ-1≤χ′(G)≤χ(λ,1)(G)+,其中χ′(G)是G的正常边色数,并确定了几个特殊图类的瑕色数. |
| 关 键 词： | 边着色 全着色 瑕着色 |
On Flaw Colourings of Graphs |
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| YAO Ming,YAO Bing,XIE Jian-min,ZHANG Zhong-fu.On Flaw Colourings of Graphs[J].Journal of Gansu Normal College,2009,14(2). | |
| Authors: | YAO Ming YAO Bing XIE Jian-min ZHANG Zhong-fu |
| Institution: | 1.Department of Information Process and Control Engineering;Lanzhou Petrochemical College of Vocational Technology;Lanzhou Gansu 730060;2.College of Mathematics and Information Science;Northwest Normal University;Lanzhou Gansu 730070;3.College of Mathematics;Lanzhou City University;Lanzhou Gansu 730070 |
| Abstract: | A(λ,β)-flaw k-edge colouring of a connected graph G=(V,E) is a mapping from E to {1,2,…,k} if there is a smallest integer β≥1 such that for every colour j∈{1,2,…,β} there is at least a vertex uj∈V(G)that is incident with λ edges coloured by colour j,and for each color l∈{β+1,…,k} no two edges incident with any vertex v∈V(G)receive the colour l.The(λ,β)-flaw chromatic index of G,denoted by χ(λ,β()G),is the smallest number such that G admits a(λ,β)-flaw k-edge colouring for each k≥χ(λ,β()G).We deduce χ(λ,1)(G)+λ-1≤χ′(G)≤χ(λ,1)(G)+λ,there χ′(G) is the proper chromatic index of G,and determine(λ,β)-flaw chromatic indices for some particular graphs. |
| Keywords: | edge colouring total colouring flaw colouring |
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