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- W3155234169 abstract "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." @default.
- W3155234169 created "2021-04-26" @default.
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- W3155234169 date "2021-09-01" @default.
- W3155234169 modified "2023-09-27" @default.
- W3155234169 title "Extremal stretch of proper-walk coloring of graphs" @default.
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- W3155234169 doi "https://doi.org/10.1016/j.amc.2021.126240" @default.
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