| 关于偏序集相关联图的色数 |
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| 引用本文： | 薛占军,刘三阳. 关于偏序集相关联图的色数[J]. 纯粹数学与应用数学, 2010, 26(4): 615-619,625. DOI: 10.3969/j.issn.1008-5513.2010.04.015 |
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| 作者姓名： | 薛占军 刘三阳 |
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| 作者单位： | 西安电子科技大学数学系,陕西,西安,710071;西安电子科技大学数学系,陕西,西安,710071 |
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| 基金项目： | 国家自然科学基金，国家重点实验室综合业务网络基金 |
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| 摘 要： | 对于每一个含有最小元素0的偏序集（P,≤）可以得到一个与其关联的图G（P）.本文主要通过代数的方法研究了所得关联图G（P）的性质,证明了如果G（P）的色数和团数是有限的,那么色数和团数都仅比P的极小素理想的个数大1.
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| 关 键 词： | 偏序集 色数 团数 理想 |
On chromatic number of associated graphs of partially ordered set |
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| XUE Zhan-jun,LIU San-yang. On chromatic number of associated graphs of partially ordered set[J]. Pure and Applied Mathematics, 2010, 26(4): 615-619,625. DOI: 10.3969/j.issn.1008-5513.2010.04.015 |
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| Authors: | XUE Zhan-jun LIU San-yang |
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| Affiliation: | XUE Zhan-jun,LIU San-yang(Department of Mathematics,Xidian University,Xi'an 710071,China) |
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| Abstract: | For any partially ordered set（P,≤） with a least element 0,there is a graph associated to it.The main purpose of this paper is using an algebraic method to study the properties of the associated graphs.It is proved that if the chromatic number and the clique number of the associated graph are finite,then they are both larger than the number of minimal prime ideals of P only one. |
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| Keywords: | partially ordered set chromatic number clique number ideal |
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