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Note on directed proper connection number of a random graph

Author

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  • Gu, Ran
  • Deng, Bo
  • Li, Rui

Abstract

For an arc-colored digraph D, we say D is properly strongly connected, if for any ordered pair of vertices (x, y), D contains a directed path from x to y such that any adjacent arcs in that path have distinct colors. The directed proper connection number pc→(D) of a digraph D, is the minimum number of colors to make D properly strongly connected. Let D(n, p) denote the random digraph model, in which every arc of a digraph is chosen with probability p independently from other arcs. We prove that if p={logn+loglogn+λ(n)}/n, then with high probability, pc→(D(n,p))=2, where λ(n) tends to infinite.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:169-174
    DOI: 10.1016/j.amc.2019.05.028
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    References listed on IDEAS

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    1. Hui Lei & Shasha Li & Henry Liu & Yongtang Shi, 2018. "Rainbow vertex connection of digraphs," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 86-107, January.
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    Cited by:

    1. Li, Zhenzhen & Wu, Baoyindureng, 2022. "Proper-walk connection of hamiltonian digraphs," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    2. Fiedorowicz, Anna & Sidorowicz, Elżbieta & Sopena, Éric, 2021. "Proper connection and proper-walk connection of digraphs," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    3. Nie, Kairui & Ma, Yingbin & Sidorowicz, Elżbieta, 2023. "(Strong) Proper vertex connection of some digraphs," Applied Mathematics and Computation, Elsevier, vol. 458(C).

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