| 图的星边星-全色数的一个上界 |
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| 引用本文： | 刘信生,孙春虎,王志强.图的星边星-全色数的一个上界[J].兰州理工大学学报,2012,38(1):129-135. |
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| 作者姓名： | 刘信生 孙春虎 王志强 |
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| 作者单位： | 西北师范大学数学与信息科学学院,甘肃兰州,730070 |
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| 基金项目： | 国家自然科学基金，甘肃省教育厅基金 |
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| 摘 要： | 提出图的星边星-全染色的概念,图G的一个正常全染色被称为星边星-全染色,如果对G中点进行星染色,边进行星边染色.并定义图的星边星-全色数,记为χsTs(G).用构造染色的方法给出一些特殊图(路,圈,轮,扇,完全图)的星边星-全色数.同时运用概率方法给出满足一定条件的图G的星边星-全色数的一个上界,即若图G的最大度Δ(G)≥30,则χsTs(G)≤24(Δ-1)3/2.
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| 关 键 词： | 星边星-全染色 星边星-全色数 概率方法 Lovász局部引理 |
An upper bound of star-edge-star total chromatic number of graphs |
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| LIU Xin-sheng
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SUN Chun-hu
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WANG Zhi-qiang.An upper bound of star-edge-star total chromatic number of graphs[J].Journal of Lanzhou University of Technology,2012,38(1):129-135. |
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| Authors: | LIU Xin-sheng SUN Chun-hu WANG Zhi-qiang |
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| Institution: | (College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China) |
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| Abstract: | A concept of star-edge-star total coloring of graphs was presented.A proper total coloring of a graph G would be called star-edge-star total coloring if its vertices were star coloring and its edges were star-edge coloring.The star-edge-star total chromatic number of G was defined and denoted by χTss(G).The star-edge-star total chromatic number of some particular graphs(path,cycle,wheel,fan,complete graph) were given by using the method of coloring construction.Meantime,an upper bound of star-edge-star total chromatic number of graph which satisfied definite conditions,was given by means of probabilistic method,namely χTss(G)≤24(Δ-1)3/2 for a graph G if its maximum degree Δ(G)≥30. |
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| Keywords: | star-edge-star total coloring star-edge-star total chromatic number probabilistic method Lovász local lemma |
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