运筹学学报
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梁作松1,*
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基金资助:
国家自然科学基金(No. 11601262), 山东省自然科学青年基金 (No. ZR2014AQ008), 中国博士后基金(No. 2016M592156)
LIANG Zuosong1,*
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摘要:
设G=(V,E)为简单图, G的每个至少有两个顶点的极大完全子图称为G的一个团. 图的团染色定义为给图的点进行染色使得图中没有单一颜色的团, 也就是说每一个团具有至少2种颜色. 图的一个k-团染色 是指用k 种颜色给图的点着色使得图G 的每一个团至少有2种颜色. 图G的团染色数\chi_{C}(G)是指最小的数k使得图G 存在k-团染色. 首先指出了完全图的线图的团染色数与推广的Ramsey 数之间的一个联系, 其次对于最大度不超过7的线图给出了一个最优团染色的多项式时间算法.
关键词: 团染色, 多项式时间算法, 线图, 完全图
Abstract:
A clique is defined as a complete subgraph maximal under inclusion and having at least two vertices. A k-clique-coloring of a graph G is an assignment of k colors to the vertices of G such that no clique of G is monochromatic. If G has a k-clique-coloring, we say that G is k-clique-colorable. The clique-coloring number \chi_{C}(G) is the smallest integer k admitting a k-clique-coloring of G. In this paper, we first point out a relation between the clique-coloring number of line graphs of complete graphs and the generalized Ramsey number. Secondly, we give a polynomial time algorithm for the optimal clique-coloring problem in line graphs of maximum degree at most 7.
Key words: clique-coloring, polynomial-time algorithm, line graph, complete graph
梁作松. 线图上的团染色问题[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2016.03.010.
LIANG Zuosong. The clique-coloring problem in line graphs[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2016.03.010.
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链接本文: https://www.ort.shu.edu.cn/CN/10.15960/j.cnki.issn.1007-6093.2016.03.010
https://www.ort.shu.edu.cn/CN/Y2016/V20/I3/92