| 点可区别边色数和点可区别全色数的两个上界 |
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| 引用本文： | 安明强,孟祥波.点可区别边色数和点可区别全色数的两个上界[J].天津科技大学学报,2011,26(1):75-78. |
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| 作者姓名： | 安明强 孟祥波 |
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| 作者单位： | 天津科技大学理学院,天津,300457 |
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| 基金项目： | 天津科技大学科学研究基金 |
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| 摘 要： | 应用概率方法中的第一矩量原理和Markov不等式,证明了对于最大度为Δ的n阶图G,当Δ≥2时,其点可区别的边色数χv′d(G)≤nΔ(n-1),当n≥3,Δ≥1时,其点可区别的全色数χvt(G)≤2 nΔ(n-1).
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| 关 键 词： | 边染色 全染色 点可区别边色数 点可区别全色数 概率方法 |
Two Upper Bounds for the Vertex-Distinguishing-Edge Chromatic Numbers and Vertex-Distinguishing-Total Chromatic Numbers |
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| AN Ming-qiang,MENG Xiang-bo.Two Upper Bounds for the Vertex-Distinguishing-Edge Chromatic Numbers and Vertex-Distinguishing-Total Chromatic Numbers[J].Journal of Tianjin University of Science & Technology,2011,26(1):75-78. |
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| Authors: | AN Ming-qiang MENG Xiang-bo |
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| Institution: | AN Ming-qiang,MENG Xiang-bo(College of Science,Tianjin University of Science & Technology,Tianjin 300457,China) |
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| Abstract: | It was proved that every graph with n vertices and with maximum degree Δ≥ 2 has a vertex distinguishing edge coloring with at most nΔ(n? 1)colors by using the first moment principle and Markov’s inequality of probabilistic method.It was also proved that every graph with n≥ 3 vertices and with maximum degree Δ≥ 1 has a vertex distinguishing total coloring with at most 2 nΔ(n? 1)colors. |
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| Keywords: | edge coloring total coloring vertex distinguishing edge chromatic number vertex distinguishing total chromatic number probabilistic method |
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