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Proper-walk connection of hamiltonian digraphs

Author

Listed:
  • Li, Zhenzhen
  • Wu, Baoyindureng

Abstract

Under an arc-coloring c of a digraph D, if for each pair of vertices (u,v), there exists a directed walk from u to v satisfying that any two consecutive arcs of it have different colors, we say that D is properly-walk connected, and c is a proper-walk coloring of D. The proper-walk connection number wc→(D) of D is the least integer k such that D has a proper-walk coloring with k colors.

Suggested Citation

  • Li, Zhenzhen & Wu, Baoyindureng, 2022. "Proper-walk connection of hamiltonian digraphs," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    • Handle: RePEc:eee:apmaco:v:427:y:2022:i:c:s0096300322002442
    DOI: 10.1016/j.amc.2022.127169
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    References listed on IDEAS

    as
    1. Fiedorowicz, Anna & Sidorowicz, Elżbieta & Sopena, Éric, 2021. "Proper connection and proper-walk connection of digraphs," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Gu, Ran & Deng, Bo & Li, Rui, 2019. "Note on directed proper connection number of a random graph," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 169-174.
    3. Wayne Goddard & Robert Melville, 2018. "Properly colored trails, paths, and bridges," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 463-472, February.
    Full references (including those not matched with items on IDEAS)

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