| 图的邻域并和连通的[k,k+1]-因子 |
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| 引用本文： | 刘红霞,乔贵平. 图的邻域并和连通的[k,k+1]-因子[J]. 烟台大学学报(自然科学与工程版), 2013, 26(1): 1-3 |
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| 作者姓名： | 刘红霞 乔贵平 |
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| 作者单位： | 1. 烟台大学数学与信息科学学院,山东烟台,264005
2. 山西省临县教育体育局,山西临县,033200 |
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| 基金项目： | 国家自然科学基金资助项目，山东省教育厅科技计划项目，烟台大学博士基金 |
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| 摘 要： | 设G是阶为n的图.F是G的支撑子图且对所有的x∈V(G)都有k≤dF(x)≤k+1,则称F为G的[k,k+1]-因子.一个[k,k+1]-因子如果连通,则称为连通的[k,k+1]-因子.一个[k,k+1]-因子若包含一个哈密顿圈,则称为哈密顿[k,k+1]-因子.给出了图有哈密顿[k,k+1]-因子或连通的[k,k+1]-因子关于邻域并的若干新的充分条件.
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| 关 键 词： | 图 [k,k+1]-因子 连通因子 邻域并 |
Neighborhood Union and Connected [k, k + 1]-Factors in Graphs |
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| LIU Hong-xia , QIAO Gui-ping. Neighborhood Union and Connected [k, k + 1]-Factors in Graphs[J]. Journal of Yantai University(Natural Science and Engineering edirion), 2013, 26(1): 1-3 |
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| Authors: | LIU Hong-xia QIAO Gui-ping |
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| Affiliation: | 1. School of Mathematics and Information Science, Yantai University, Yantai 264005, China; 2. Education and Sports Bureau of Lin County, Lin County 033200, China) |
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| Abstract: | Let G be a graph of order n. A spanning subgraph F of G is called a[ k, k ＋ 1 ] -factor if k ≤ dF （x） k ＋ 1 holds for each x ∈ V（G）. A [ k, k ＋ 1]-factor is called a connected [ k, k ＋ 1 ] -factor if it is connected. A [ k, k ＋ 1 ] -factor F is called a Hamilton [ k, k ＋ 1 ] -factor if F contains a Hamilton cycle. In this paper, sev- eralsufficient conditions related to neighborhood union for graphs to have connected [ k, k ＋ 1 ] -factors or Hamilton [ k, k ＋ 1 ] -factors are given. |
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| Keywords: | graph [ k, k ＋ 1 ] -factor connected factor neighborhood union |
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