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Rainbow vertex connection of digraphs

Author

Listed:
  • Hui Lei

    (Nankai University)

  • Shasha Li

    (Zhejiang University)

  • Henry Liu

    (Central South University)

  • Yongtang Shi

    (Nankai University)

Abstract

An edge-coloured path is rainbow if its edges have distinct colours. An edge-coloured connected graph is said to be rainbow connected if any two vertices are connected by a rainbow path, and strongly rainbow connected if any two vertices are connected by a rainbow geodesic. The (strong) rainbow connection number of a connected graph is the minimum number of colours needed to make the graph (strongly) rainbow connected. These two graph parameters were introduced by Chartrand et al. (Math Bohem 133:85–98, 2008). As an extension, Krivelevich and Yuster proposed the concept of rainbow vertex-connection. The topic of rainbow connection in graphs drew much attention and various similar parameters were introduced, mostly dealing with undirected graphs. Dorbec, Schiermeyer, Sidorowicz and Sopena extended the concept of the rainbow connection to digraphs. In this paper, we consider the (strong) rainbow vertex-connection number of digraphs. Results on the (strong) rainbow vertex-connection number of biorientations of graphs, cycle digraphs, circulant digraphs and tournaments are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:1:d:10.1007_s10878-017-0156-7
    DOI: 10.1007/s10878-017-0156-7
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    Citations

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    Cited by:

    1. Ma, Yingbin & Nie, Kairui & Jin, Fengxia & Wang, Cui, 2019. "Total rainbow connection numbers of some special graphs," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 213-220.
    2. Nie, Kairui & Ma, Yingbin & Sidorowicz, Elżbieta, 2023. "(Strong) Proper vertex connection of some digraphs," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    3. 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.
    4. Fiedorowicz, Anna & Sidorowicz, Elżbieta & Sopena, Éric, 2021. "Proper connection and proper-walk connection of digraphs," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    5. Ma, Yingbin & Zhang, Xiaoxue, 2023. "Graphs with (strong) proper connection numbers m−3 and m−4," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    6. Ma, Yingbin & Zhu, Wenhan, 2022. "Some results on the 3‐total‐rainbow index," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    7. Guan, Xiaxia & Xue, Lina & Cheng, Eddie & Yang, Weihua, 2019. "Minimum degree and size conditions for the proper connection number of graphs," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 205-210.
    8. Li, Shasha & Zhao, Yan & Li, Fengwei & Gu, Ruijuan, 2019. "The generalized 3-connectivity of the Mycielskian of a graph," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 882-890.
    9. Yingbin Ma & Kairui Nie, 2021. "(Strong) Total proper connection of some digraphs," Journal of Combinatorial Optimization, Springer, vol. 42(1), pages 24-39, July.

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