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Extremal stretch of proper-walk coloring of graphs

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  • Qin, Zhongmei
  • Zhang, Junxue

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.

Suggested Citation

  • Qin, Zhongmei & Zhang, Junxue, 2021. "Extremal stretch of proper-walk coloring of graphs," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    • Handle: RePEc:eee:apmaco:v:405:y:2021:i:c:s0096300321003301
    DOI: 10.1016/j.amc.2021.126240
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    References listed on IDEAS

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    1. Wayne Goddard & Robert Melville, 2018. "Properly colored trails, paths, and bridges," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 463-472, February.
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