| 无相交三角形平面图的邻点可区别边染色 |
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| 引用本文： | 刘卓雅,徐常青.无相交三角形平面图的邻点可区别边染色[J].山东大学学报(理学版),2020,55(9):36-41. |
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| 作者姓名： | 刘卓雅 徐常青 |
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| 作者单位： | 河北工业大学理学院,天津300401;河北工业大学理学院,天津300401 |
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| 基金项目： | 国家自然科学基金资助项目(11671232) |
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| 摘 要： | 图G的k-邻点可区别边染色是指G的一个正常k-边染色满足对任意相邻顶点u和v,与u关联的边所染颜色集合和与v关联的边所染颜色集合不同。使G有k-邻点可区别边染色的k的最小值称为G的邻点可区别边色数,记作χ'a(G)。通过运用权转移方法研究了无相交三角形平面图的邻点可区别边色数,证明了若图G为无相交三角形平面图,则χ'a(G)≤max{Δ(G)+2,10}。
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| 关 键 词： | 平面图 邻点可区别边染色 邻点可区别边色数 |
Adjacent vertex distinguishing edge coloring of planar graphs without intersecting triangles |
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| LIU Zhuo-ya,XU Chang-qing.Adjacent vertex distinguishing edge coloring of planar graphs without intersecting triangles[J].Journal of Shandong University,2020,55(9):36-41. |
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| Authors: | LIU Zhuo-ya XU Chang-qing |
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| Institution: | School of Science, Hebei University of Technology, Tianjin 300401, China |
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| Abstract: | A k-adjacent vertex distinguishing edge coloring of a graph G is a proper k-edge coloring of G such that for any two adjacent vertices u and v, the color set of edges incident with u is different from the color set of edges incident with v. The least k for a k-adjacent vertex distinguishing edge coloring of G is the adjacent vertex distinguishing chromatic number, denoted by χ'a(G). By using the discharging method, we study the adjacent vertex distinguishing chromatic number of a planar graph without intersecting triangles, and get the conclusion: if G is a planar graph without intersecting triangles, then χ'a(G)≤max{Δ(G)+2,10}. |
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| Keywords: | planar graph adjacent vertex distinguishing edge coloring adjacent vertex distinguishing chromatic number |
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