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山东大学学报(工学版) ›› 2015, Vol. 45 ›› Issue (1): 64-69.doi: 10.6040/j.issn.1672-3961.0.2014.293

• 控制科学与工程 • 上一篇    下一篇

Conflict-free着色问题及其在频率分配中的应用

徐美荣1,2, 王玉振1   

  1. 1. 山东大学控制科学与工程学院, 山东 济南 250061;
    2. 济南大学数学科学学院, 山东 济南 250022
  • 收稿日期:2014-10-16 修回日期:2015-01-13 发布日期:2014-10-16
  • 通讯作者: 王玉振(1963-),男,山东泰安人,教授,博导,博士,主要研究方向为非线性控制,Hamilton控制系统理论,逻辑动态网络,复杂系统.E-mail:yzwang@sdu.edu.cn E-mail:yzwang@sdu.edu.cn
  • 作者简介:徐美荣(1973-),女,江苏徐州人,副教授,博士研究生,主要研究方向为图着色,频率分配.E-mail:ss_xumr@ujn.edu.cn
  • 基金资助:
    国家自然科学基金 (G61374065,G61374002,G61034007); 山东省泰山学者项目基金

Conflict-free coloring problem with appliction to frequency assignment

XU Meirong1,2, WANG Yuzhen1   

  1. 1. School of Control Science and Engineering, Shandong University, Jinan 250061, China;
    2. School of Mathematical Sciences, University of Jinan, Jinan 250022, China
  • Received:2014-10-16 Revised:2015-01-13 Published:2014-10-16

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摘要： 研究了超图的conflict-free着色问题。利用矩阵半张量积方法给出了conflict-free着色的两个充要条件,建立了一个可以确定出所有conflict-free着色方案的新算法。把结果应用于频率分配问题,说明了理论结果的有效性和应用性。

关键词: 半张量积, 代数公式, Conflict-free着色, 超图, 频率分配

Abstract: The conflict-free coloring problem of hypergraphs was investigated, and some new results and algorithms were obtained. Using the semi-tensor product method, two necessary and sufficient conditions were proposed for the conflict-free coloring problem based on which a new algorithm was established to find all the conflict-free coloring schemes for any hypergraph. Then the theoretical results were applied to the frequency assignment problem to show its effectiveness and applicability.

Key words: semi-tensor product, algebraic formula, conflict-free coloring, hypergraph, frequency assignment

中图分类号: 

  • TN915
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