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Extremal stretch of proper-walk coloring of graphs
Applied Mathematics and Computation ( IF 3.5 ) Pub Date : 2021-04-13 , DOI: 10.1016/j.amc.2021.126240
Zhongmei Qin , Junxue Zhang

Let G be an edge-colored connected graph, a path (trail, walk) of G is said to be a proper-path (trail, walk) if any two adjacent edges of it are colored distinctly. If there is a proper-path (trail, walk) between each pair of different vertices of G, then G is called proper-path (trail, walk) connected. The edge-coloring which makes G proper-path (trail, walk) connected is called a proper-path (trail, walk) coloring. The minimum number of colors required in a proper-path (trail, walk) coloring is referred to as the proper-path (trail, walk) connection number of G. In J. Bang-Jensen, T. Bellitto and A. Yeo, Proper-walk connection number of graphs, J. Graph Theory 96(2020) 137–159, the authors investigated the graphs with proper-walk connection number k and suggested to study the stretch of proper-walk coloring. In this note, we consider the stretch of proper-walk (path, trail) coloring and present some tight upper bounds.



中文翻译:

图的正确游动着色的极端拉伸

G 是一个边色的连通图,一条路径(小径,步行) G如果它的任何两个相邻边缘都有明显的颜色,则被称为一条正确的路径(小径,步行)。如果在的每对不同的顶点之间都有一条正确的路径(小径,步行)G 然后 G称为连接的正确路径(小径,步行)。边缘着色G连接的正确路径(步道,步道)称为适当路径(步道,步道)着色。适当路径(步道,步行)着色所需的最小颜色数称为适当路径(步道,步行)着色的连接数。G。在J. Bang-Jensen,T。Bellitto和A. Yeo的“图的正确行走连接数”,《 J。图论》 96(2020)137–159中,作者研究了具有正确行走连接数的图ķ并建议研究适当的步法着色的范围。在本说明中,我们考虑了适当的步行(路径,步道)着色的范围,并提出了一些严格的上限。

更新日期:2021-04-13
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